bluuebunny/crossref_metadata_2025 huggingface dataset:
The C2A domain of synaptotagmin-like protein 3 (Slp3) is an atypical calcium-dependent phospholipid-binding machine: comparison with the C2A domain of synaptotagmin I
Authors: FUKUDA Mitsunori
Published: September 2002

The synaptotagmin-like protein (Slp) family consists of an N-terminal Rab27-binding domain and C-terminal tandem C2 motifs, and although it has been suggested to regulate Rab27-dependent membrane trafficking, such as Ca2+-regulated granule exocytosis in T-lymphocytes [Kuroda, Fukuda, Ariga and Mikoshiba (2002) J. Biol. Chem. 277, 9212–9218], little is known about the Ca2+-binding property of the Slp family. In this study, I demonstrated that the C2A domain of Slp3 exhibits Ca2+-dependent phospholipid-binding activity similar to that of the C2A domain of synaptotagmin I (Syt I) with regard to phospholipid selectivity, bivalent cation selectivity and effect of ionic strength. This finding was surprising because the C2A domains of other C-terminal-type (C-type) tandem C2 proteins require five conserved acidic residues in the putative Ca2+-binding loops 1 and 3 on the top of the β-sandwich structure for their Ca2+-/phospholipid-binding activity, whereas the C2A domain of Slp3 contains only one conserved acidic residue in the putative Ca2+-binding loop 1. Site-directed mutagenesis and chimaeric analysis of the C2A domains of Syt I and Slp3 showed that Glu-336 and Glu-337 in the putative Ca2+-binding loop 1 and polybasic sequence (Lys-359, Lys-360 and Lys-361) in the β-4 strand of the C2 structure are crucial for Ca2+-dependent phospholipid-binding activity of the Slp3 C2A domain, whereas the similar polybasic sequence in the C2A domain of Syt I is dispensable for Ca2+-dependent phospholipid-binding activity. These results indicate that the C2A domain of Slp3 is an atypical Ca2+-/phospholipid-binding machine, compared with other C-type tandem C2 proteins.
Functional analysis of the C-terminal boundary of the second nucleotide binding domain of the cystic fibrosis transmembrane conductance regulator and structural implications
Authors: GENTZSCH Martina , ALEKSANDROV Andrei , ALEKSANDROV Luba , RIORDAN John R.
Published: September 2002

The cystic fibrosis transmembrane conductance regulator (CFTR) contains two nucleotide-binding domains (NBDs) or ATP-binding cassettes (ABCs) that characterize a large family of membrane transporters. Although the three-dimensional structures of these domains from several ABC proteins have been determined, this is not the case for CFTR, and hence the domains are defined simply on the basis of sequence alignment. The functional C-terminal boundary of NBD1 of CFTR was located by analysis of chloride channel function [Chan, Csanady, Seto-Young, Nairn and Gadsby (2000) J. Gen. Physiol. 116, 163–180]. However, the boundary between the C-terminal end of NBD2 and sequences further downstream in the whole protein, that are important for its cellular localization and endocytotic turnover, has not been defined. We have now done this by assaying the influence of progressive C-terminal truncations on photolabelling of NBD2 by 8-azido-ATP, which reflects hydrolysis, as well as binding, at that domain, and on NBD2-dependent channel gating itself. The boundary defined in this way is between residues 1420 and 1424, which corresponds to the final β-strand in aligned NBDs whose structures have been determined. Utilization of this information should facilitate the generation of monodisperse NBD2 polypeptides for structural analysis, which until now has not been possible. The established boundary includes within NBD2 a hydrophobic patch of four residues (1413–1416) previously shown to be essential for CFTR maturation and stability [Gentzsch and Riordan (2001) J. Biol. Chem. 276, 1291–1298]. This hydrophobic cluster is conserved in most ABC proteins, and on alignment with ones of known structure constitutes the penultimate β-strand of the domain which is likely to participate in essential structure-stabilizing β-sheet formation.
Small interfering RNAs as a tool to assign Rho GTPase exchange-factor function in vivo
Authors: GAMPEL Alexandra , MELLOR Harry
Published: September 2002

Rho GTPases control a complex network of intracellular signalling pathways. Whereas progress has been made in identifying downstream signalling partners for these proteins, the characterization of Rho upstream regulatory guanine-nucleotide exchange factors (GEFs) has been hampered by a lack of suitable research tools. Here we use small interfering RNAs (siRNAs) to examine the cellular regulation of the RhoB GTPase, and show that RhoB is activated downstream of the epidermal-growth-factor receptor through the Vav2 exchange factor. These studies demonstrate that siRNAs are an ideal research tool for the assignment of Rho GEF function in vivo.
Involutions fixing ℝℙ^{𝕠𝕕𝕕}⊔ℙ(𝕙,𝕚), I
Authors: Lü Zhi
Published: September 2002

This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space

R
P

j

\mathbb {RP}^j

with its normal bundle nonbounding and a Dold manifold

P
(
h
,
i
)

P(h,i)

with

h
>
0

h>0

and

i
>
0

i>0

. For odd

h
h

, the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of

P
(
h
,
i
)

P(h,i)

may not be best possible; for even

h
h

, the problem may be reduced to the problem for even projective spaces.
Amenability and exactness for dynamical systems and their 𝐶*-algebras
Authors: Anantharaman-Delaroche Claire
Published: September 2002

We study the relations between amenability (resp. amenability at infinity) of

C

∗

C^{*}

-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
Trees and branches in Banach spaces
Authors: Odell E. , Schlumprecht Th.
Published: September 2002

An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree

T

\mathcal {T}

of a certain type on a space

X
X

is presumed to have a branch with some property. It is shown that then

X
X

can be embedded into a space with an FDD

(

E
i

)

(E_i)

so that all normalized sequences in

X
X

which are almost a skipped blocking of

(

E
i

)

(E_i)

have that property. As an application of our work we prove that if

X
X

is a separable reflexive Banach space and for some

1
>
p
>
∞

1>p>\infty

and

C
>
∞

C>\infty

every weakly null tree

T

\mathcal {T}

on the sphere of

X
X

has a branch

C
C

-equivalent to the unit vector basis of

ℓ
p

\ell _p

, then for all

ε
>
0

\varepsilon >0

, there exists a subspace of

X
X

having finite codimension which

C
2

+
ε

C^2+\varepsilon

embeds into the

ℓ
p

\ell _p

sum of finite dimensional spaces.
Associated primes of graded components of local cohomology modules
Authors: Brodmann Markus , Katzman Mordechai , Sharp Rodney
Published: September 2002

The

i
i

-th local cohomology module of a finitely generated graded module

M
M

over a standard positively graded commutative Noetherian ring

R
R

, with respect to the irrelevant ideal

R
+

R_+

, is itself graded; all its graded components are finitely generated modules over

R
0

R_0

, the component of

R
R

of degree

0
0

. It is known that the

n
n

-th component

H

R
+

i

(
M

)
n

H^i_{R_+}(M)_n

of this local cohomology module

H

R
+

i

(
M
)

H^i_{R_+}(M)

is zero for all

n
>>
0

n>> 0

. This paper is concerned with the asymptotic behaviour of

Ass

R
0

⁡
(

H

R
+

i

(
M

)
n

)

\operatorname {Ass}_{R_0}(H^i_{R_+}(M)_n)

as

n
→
−
∞

n \rightarrow -\infty

. The smallest

i
i

for which such study is interesting is the finiteness dimension

f
f

of

M
M

relative to

R
+

R_+

, defined as the least integer

j
j

for which

H

R
+

j

(
M
)

H^j_{R_+}(M)

is not finitely generated. Brodmann and Hellus have shown that

Ass

R
0

⁡
(

H

R
+

f

(
M

)
n

)

\operatorname {Ass}_{R_0}(H^f_{R_+}(M)_n)

is constant for all

n
>>
0

n > > 0

(that is, in their terminology,

Ass

R
0

⁡
(

H

R
+

f

(
M

)
n

)

\operatorname {Ass}_{R_0}(H^f_{R_+}(M)_n)

is asymptotically stable for

n
→
−
∞

n \rightarrow -\infty

). The first main aim of this paper is to identify the ultimate constant value (under the mild assumption that

R
R

is a homomorphic image of a regular ring): our answer is precisely the set of contractions to

R
0

R_0

of certain relevant primes of

R
R

whose existence is confirmed by Grothendieck’s Finiteness Theorem for local cohomology. Brodmann and Hellus raised various questions about such asymptotic behaviour when

i
>
f

i > f

. They noted that Singh’s study of a particular example (in which

f
=
2

f = 2

) shows that

Ass

R
0

⁡
(

H

R
+

3

(
R

)
n

)

\operatorname {Ass}_{R_0}(H^3_{R_+}(R)_n)

need not be asymptotically stable for

n
→
−
∞

n \rightarrow -\infty

. The second main aim of this paper is to determine, for Singh’s example,

Ass

R
0

⁡
(

H

R
+

3

(
R

)
n

)

\operatorname {Ass}_{R_0}(H^3_{R_+}(R)_n)

quite precisely for every integer

n
n

, and, thereby, answer one of the questions raised by Brodmann and Hellus.
Character degrees and nilpotence class of finite 𝑝-groups: An approach via pro-𝑝 groups
Authors: Jaikin-Zapirain A. , Moretó Alexander
Published: September 2002

LetS\mathcal {S}be a finite set of powers ofppcontaining 1. It is known that for some choices ofS\mathcal {S}, ifPPis a finitepp-group whose set of character degrees isS\mathcal {S}, then the nilpotence class ofPPis bounded by some integer that depends onS\mathcal {S}, while for some other choices ofS\mathcal {S}such an integer does not exist. The sets of the first type are called class bounding sets. The problem of determining the class bounding sets has been studied in several papers whose results made it tempting to conjecture that a setS\mathcal {S}is class bounding if and only ifp∉Sp\notin \mathcal {S}. In this article we provide a new approach to this problem. Our main result shows the relevance of certainpp-adic space groups in this problem. With its help, we are able to prove some results that provide new class bounding sets. We also show that there exist non-class-bounding setsS\mathcal {S}such thatp∉Sp\notin \mathcal {S}.
Functional Calculus in Hölder-Zygmund Spaces
Authors: Bourdaud G. , Lanza de Cristoforis Massimo
Published: September 2002

In this paper we characterize those functions

f
f

of the real line to itself such that the nonlinear superposition operator

T

f

T_{f}

defined by

T

f

[
g
]
:=
f
∘
g

T_{f}[ g]:= f\circ g

maps the Hölder-Zygmund space

S

s

(

R

n

)

\mathcal {S}^s(\mathbf {R}^n)

to itself, is continuous, and is

r
r

times continuously differentiable. Our characterizations cover all cases in which

s
s

is real and

s
>
0

s>0

, and seem to be novel when

s
>
0

s>0

is an integer.
Critical Heegaard surfaces
Authors: Bachman David
Published: September 2002

In this paper we introduce critical surfaces, which are described via a 1-complex whose definition is reminiscent of the curve complex. Our main result is that if the minimal genus common stabilization of a pair of strongly irreducible Heegaard splittings of a 3-manifold is not critical, then the manifold contains an incompressible surface. Conversely, we also show that if a non-Haken 3-manifold admits at most one Heegaard splitting of each genus, then it does not contain a critical Heegaard surface. In the final section we discuss how this work leads to a natural metric on the space of strongly irreducible Heegaard splittings, as well as many new and interesting open questions.
Scaling coupling of reflecting Brownian motions and the hot spots problem
Authors: Pascu Mihai
Published: September 2002

We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.
On the crossing number of positive knots and braids and braid index criteria of Jones and Morton-Williams-Franks
Authors: Stoimenow A.
Published: September 2002

We give examples of knots with some unusual properties of the crossing number of positive diagrams or strand number of positive braid representations. In particular, we show that positive braid knots may not have positive minimal (strand number) braid representations, giving a counterpart to results of Franks-Williams and Murasugi. Other examples answer questions of Cromwell on homogeneous and (partially) of Adams on almost alternating knots. We give a counterexample to, and a corrected version of, a theorem of Jones on the Alexander polynomial of 4-braid knots. We also give an example of a knot on which all previously applied braid index criteria fail to estimate sharply (from below) the braid index. A relation between (generalizations of) such examples and a conjecture of Jones that a minimal braid representation has unique writhe is discussed. Finally, we give a counterexample to Morton’s conjecture relating the genus and degree of the skein polynomial.
Spectral asymptotics for Sturm-Liouville equations with indefinite weight
Authors: Binding Paul , Browne Patrick , Watson Bruce
Published: September 2002

The Sturm-Liouville equation

−
(
p

y
′

)
′

+
q
y
=
λ
r
y

on

[
0
,
l
]

\begin{equation*} -(py’)’ + qy =\lambda ry \;\; \text {on}\;\; [0,l] \end{equation*}

is considered subject to the boundary conditions
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row 1st Column y left-parenthesis 0 right-parenthesis cosine alpha 2nd Column a m p semicolon equals left-parenthesis p y Superscript prime Baseline right-parenthesis left-parenthesis 0 right-parenthesis sine alpha comma 2nd Row 1st Column y left-parenthesis l right-parenthesis cosine beta 2nd Column a m p semicolon equals left-parenthesis p y Superscript prime Baseline right-parenthesis left-parenthesis l right-parenthesis sine beta period EndLayout">

y
(
0
)
cos
⁡
α

a
m
p
;
=
(
p

y
′

)
(
0
)
sin
⁡
α
,

y
(
l
)
cos
⁡
β

a
m
p
;
=
(
p

y
′

)
(
l
)
sin
⁡
β
.

\begin{align*} y(0)\cos \alpha &= (py’)(0)\sin \alpha ,\\ y(l)\cos \beta &= (py’)(l)\sin \beta . \end{align*}

We assume that

p
p

is positive and that

p
r

pr

is piecewise continuous and changes sign at its discontinuities. We give asymptotic approximations up to

O
(
1

/

n

)

O(1/\sqrt {n})

for

λ
n

\sqrt {\lambda _n}

, or equivalently up to

O
(

n

)

O(\sqrt {n})

for

λ
n

\lambda _n

, the eigenvalues of the above boundary value problem.
A theory of concordance for non-spherical 3-knots
Authors: Blanlœil Vincent , Saeki Osamu
Published: September 2002

Consider a closed connected oriented 3-manifold embedded in the

5
5

-sphere, which is called a

3
3

-knot in this paper. For two such knots, we say that their Seifert forms are spin concordant, if they are algebraically concordant with respect to a diffeomorphism between the 3-manifolds which preserves their spin structures. Then we show that two simple fibered 3-knots are geometrically concordant if and only if they have spin concordant Seifert forms, provided that they have torsion free first homology groups. Some related results are also obtained.
Embeddings up to homotopy of two-cones in euclidean space
Authors: Lambrechts Pascal , Stanley Don , Vandembroucq Lucile
Published: September 2002

We say that a finite CW-complex

X
X

embeds up to homotopy in a sphere

S

n
+
1

S^{n+1}

if there exists a subpolyhedron

K
⊂

S

n
+
1

K\subset S^{n+1}

having the homotopy type of

X
X

. The main result of this paper is a sufficient condition for the existence of such a homotopy embedding in a given codimension when

X
X

is a simply-connected two-cone (a two-cone is the homotopy cofibre of a map between two suspensions). We give different applications of this result: we prove that if

X
X

is a two-cone then there are no rational obstructions to embeddings up to homotopy in codimension 3. We give also a description of the homotopy type of the boundary of a regular neighborhood of the embedding of a two-cone in a sphere. This enables us to construct a closed manifold

M
M

whose Lusternik-Schnirelmann category and cone-length are not affected by removing one point of

M
M

.
Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains
Authors: Pan Xing-Bin , Kwek Keng-Huat
Published: September 2002

We establish an asymptotic estimate of the lowest eigenvalue

μ
(
b

F

)

\mu (b\mathbf {F})

of the Schrödinger operator

−

∇

b

F

2

-\nabla _{b\mathbf {F}}^{2}

with a magnetic field in a bounded

2
2

-dimensional domain, where curl

F

\mathbf {F}

vanishes non-degenerately, and

b
b

is a large parameter. Our study is based on an analysis on an eigenvalue variation problem for the Sturm-Liouville problem. Using the estimate, we determine the value of the upper critical field for superconductors subject to non-homogeneous applied magnetic fields, and localize the nucleation of superconductivity.
The space of (𝜓,𝛾)–additive mappings on semigroups
Authors: Faĭziev Valeriĭ , Rassias Themistocles , Sahoo Prasanna
Published: September 2002

In this paper, we introduce the concept of

(
ψ
,
γ
)

(\psi ,\gamma )

–pseudoadditive mappings from a semigroup into a Banach space, and we provide a generalized solution of Ulam’s problem for approximately additive mappings.
Inequalities for decomposable forms of degree 𝑛+1 in 𝑛 variables
Authors: Thunder Jeffrey
Published: September 2002

We consider the number of integral solutions to the inequality

|

F
(

x

)

|

≤
m

|F(\mathbf {x}) |\le m

, where

F
(

X

)
∈

Z

[

X

]

F(\mathbf {X} )\in \mathbb {Z} [\mathbf {X} ]

is a decomposable form of degree

n
+
1

n+1

in

n
n

variables. We show that the number of such solutions is finite for all

m
m

only if the discriminant of

F
F

is not zero. We get estimates for the number of such solutions that display appropriate behavior in terms of the discriminant. These estimates sharpen recent results of the author for the general case of arbitrary degree.
Weak amenability of module extensions of Banach algebras
Authors: Zhang Yong
Published: September 2002

We start by discussing general necessary and sufficient conditions for a module extension Banach algebra to benn-weakly amenable, forn=0,1,2,⋯n = 0,1,2,\cdots. Then we investigate various special cases. All these case studies finally provide us with a way to construct an example of a weakly amenable Banach algebra which is not33-weakly amenable. This answers an open question raised by H. G. Dales, F. Ghahramani and N. Grønbæk.
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
Authors: Pantilie Radu , Wood John
Published: September 2002

We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.
Growth and ergodicity of context-free languages
Authors: Ceccherini-Silberstein Tullio , Woess Wolfgang
Published: September 2002

A language

L
L

over a finite alphabet

Σ
\boldsymbol \Sigma

is called growth-sensitive if forbidding any set of subwords

F
F

yields a sublanguage

L

F

L^{F}

whose exponential growth rate is smaller than that of

L
L

. It is shown that every ergodic unambiguous, nonlinear context-free language is growth-sensitive. “Ergodic” means for a context-free grammar and language that its dependency di-graph is strongly connected. The same result as above holds for the larger class of essentially ergodic context-free languages, and if growth is considered with respect to the ambiguity degrees, then the assumption of unambiguity may be dropped. The methods combine a construction of grammars for

2
2

-block languages with a generating function technique regarding systems of algebraic equations.
Emergence of the Witt group in the cellular lattice of rational spaces
Authors: Hess Kathryn , Parent Paul-Eugène
Published: September 2002

We give an embedding of a quotient of the Witt semigroup into the lattice of rational cellular classes represented by formal

2
2

-cones between

S

2
n

S^{2n}

and the two-cell complex

X
n

=

S

2
n

∪

[
ι
,
ι
]

e

4
n

X_n=S^{2n}\cup _{[\iota ,\iota ]}e^{4n}

(

n
≥
1

n\geq 1

).
On the Representation Theory of Lie Triple Systems
Authors: Hodge Terrell , Parshall Brian
Published: September 2002

In this paper, we take a new look at the representation theory of Lie triple systems. We consider both ordinary Lie triple systems and restricted Lie triple systems in the sense of [14]. In a final section, we begin a study of the cohomology of Lie triple systems.
Hochschild homology criteria for trivial algebra structures
Authors: Vigué-Poirrier Micheline
Published: September 2002

We prove two similar results by quite different methods. The first one deals with augmented artinian algebras over a field: we characterize the trivial algebra structure on the augmentation ideal in terms of the maximality of the dimensions of the Hochschild homology (or cyclic homology) groups. For the second result, let

X
X

be a 1-connected finite CW-complex. We characterize the trivial algebra structure on the cohomology algebra of

X
X

with coefficients in a fixed field in terms of the maximality of the Betti numbers of the free loop space.
Generalized pseudo-Riemannian geometry
Authors: Kunzinger Michael , Steinbauer Roland
Published: September 2002

Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions, we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fundamental Lemma of (pseudo-) Riemannian geometry” in this setting and define the notion of geodesics of a generalized metric. Finally, we present applications of the resulting theory to general relativity.
Gaugeability and conditional gaugeability
Authors: Chen Zhen-Qing
Published: September 2002

New Kato classes are introduced for general transient Borel right processes, for which gauge and conditional gauge theorems hold. These new classes are the genuine extensions of the Green-tight measures in the classical Brownian motion case. However, the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability. We show that gaugeability, conditional gaugeability and the subcriticality for the associated Schrödinger operators are equivalent for transient Borel right processes with strong duals. Analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric Markov processes. These analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases. Connections with the positivity of the spectral radii of the associated Schrödinger operators are also established.
A Berger-Green type inequality for compact Lorentzian manifolds
Authors: Gutiérrez Manuel , Palomo Francisco , Romero Alfonso
Published: September 2002

We give a Lorentzian metric on the null congruence associated with a timelike conformal vector field. A Liouville type theorem is proved and a boundedness for the volume of the null congruence, analogous to a well-known Berger-Green theorem in the Riemannian case, will be derived by studying conjugate points along null geodesics. As a consequence, several classification results on certain compact Lorentzian manifolds without conjugate points on its null geodesics are obtained. Finally, several properties of null geodesics of a natural Lorentzian metric on each odd-dimensional sphere have been found.
The dynamics of expansive invertible onesided cellular automata
Authors: Nasu Masakazu
Published: September 2002

Using textile systems, we prove the conjecture of Boyle and Maass that the dynamical system defined by an expansive invertible onesided cellular automaton is topologically conjugate to a topological Markov shift. We also study expansive leftmost-permutive onesided cellular automata and bipermutive endomorphisms of mixing topological Markov shifts.
An application of the Littlewood restriction formula to the Kostant-Rallis Theorem
Authors: Willenbring Jeb
Published: September 2002

Consider a symmetric pair(G,K)(G,K)of linear algebraic groups withg≅k⊕p\mathfrak {g} \cong \mathfrak {k} \oplus \mathfrak {p}, wherek\mathfrak {k}andp\mathfrak {p}are defined as the +1 and -1 eigenspaces of the involution definingKK. We view the ring of polynomial functions onp\mathfrak {p}as a representation ofKK. Moreover, setP(p)=⨁d=0∞Pd(p)\mathcal {P}(\mathfrak {p}) = \bigoplus _{d=0}^\infty \mathcal {P}^d(\mathfrak {p}), wherePd(p)\mathcal {P}^d(\mathfrak {p})is the space of homogeneous polynomial functions onp\mathfrak {p}of degreedd. This decomposition provides a gradedKK-module structure onP(p)\mathcal {P}(\mathfrak {p}). A decomposition ofPd(p)\mathcal {P}^d(\mathfrak {p})is provided for some classical families(G,K)(G,K)whenddis within a certain stable range. The stable range is defined so that the spacesPd(p)\mathcal {P}^d(\mathfrak {p})are within the hypothesis of the classical Littlewood restriction formula. The Littlewood restriction formula provides a branching rule from the general linear group to the standard embedding of the symplectic or orthogonal subgroup. Inside the stable range the decomposition ofPd(p)\mathcal {P}^d(\mathfrak {p})is interpreted as aqq–analog of the Kostant-Rallis theorem.
Tilting theory and the finitistic dimension conjectures
Authors: Angeleri-Hügel Lidia , Trlifaj Jan
Published: September 2002

Let

R
R

be a right noetherian ring and let

P

>
∞

\mathcal {P}^{>\infty }

be the class of all finitely presented modules of finite projective dimension. We prove that findim

R
=
n
>
∞

R = n > \infty

iff there is an (infinitely generated) tilting module

T
T

such that pd

T
=
n

T = n

and

T
⊥

=
(

P

>
∞

)
⊥

T ^\perp = (\mathcal P^{>\infty })^\perp

. If

R
R

is an artin algebra, then

T
T

can be taken to be finitely generated iff

P

>
∞

\mathcal P^{>\infty }

is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen-Zimmermann and Smalø.
Differential operators on a polarized abelian variety
Authors: Biswas Indranil
Published: September 2002

Let

L
L

be an ample line bundle over a complex abelian variety

A
A

. We show that the space of all global sections over

A
A

of

Diff
A

n

⁡
(
L
,
L
)

\operatorname {Diff}^{n}_A(L,L)

and

S
n

(

Diff
A
1

⁡
(
L
,
L
)
)

S^n(\operatorname {Diff}^1_A(L,L))

are both of dimension one. Using this it is shown that the moduli space

M
X

M_X

of rank one holomorphic connections on a compact Riemann surface

X
X

does not admit any nonconstant algebraic function. On the other hand,

M
X

M_X

is biholomorphic to the moduli space of characters of

X
X

, which is an affine variety. So

M
X

M_X

is algebraically distinct from the character variety if

X
X

is of genus at least one.
Universal deformation rings and Klein four defect groups
Authors: Bleher Frauke
Published: September 2002

In this paper, the universal deformation rings of certain modular representations of a finite group are determined. The representations under consideration are those which are associated to blocks with Klein four defect groups and whose stable endomorphisms are given by scalars. It turns out that these universal deformation rings are always subquotient rings of the group ring of a Klein four group over the ring of Witt vectors.
Extensions for finite Chevalley groups II
Authors: Bendel Christopher , Nakano Daniel , Pillen Cornelius
Published: September 2002

LetGGbe a semisimple simply connected algebraic group defined and split over the fieldFp{\mathbb {F}}_pwithppelements, letG(Fq)G(\mathbb {F}_{q})be the finite Chevalley group consisting of theFq{\mathbb {F}}_{q}-rational points ofGGwhereq=prq = p^r, and letGrG_{r}be therrth Frobenius kernel. The purpose of this paper is to relate extensions between modules inMod(G(Fq))\text {Mod}(G(\mathbb {F}_{q}))andMod(Gr)\text {Mod}(G_{r})with extensions between modules inMod(G)\text {Mod}(G). Among the results obtained are the following: forr>2r >2andp≥3(h−1)p\geq 3(h-1), theG(Fq)G(\mathbb {F}_{q})-extensions between two simpleG(Fq)G(\mathbb {F}_{q})-modules are isomorphic to theGG-extensions between two simpleprp^r-restrictedGG-modules with suitably “twisted" highest weights. Forp≥3(h−1)p \geq 3(h-1), we provide a complete characterization ofH1(G(Fq),H0(λ))\text {H}^{1}(G(\mathbb {F}_{q}),H^{0}(\lambda ))whereH0(λ)=indBG λH^{0}(\lambda )=\text {ind}_{B}^{G}\ \lambdaandλ\lambdaisprp^r-restricted. Furthermore, forp≥3(h−1)p \geq 3(h-1), necessary and sufficient bounds on the size of the highest weight of aGG-moduleVVare given to insure that the restriction map<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper H Superscript 1 Baseline left-parenthesis upper G comma upper V right-parenthesis right-arrow normal upper H Superscript 1 Baseline left-parenthesis upper G left-parenthesis double-struck upper F Subscript q Baseline right-parenthesis comma upper V right-parenthesis">H1⁡(G,V)→H1⁡(G(Fq),V)\operatorname {H}^{1}(G,V)\rightarrow \operatorname {H}^{1}(G(\mathbb {F}_{q}),V)is an isomorphism. Finally, it is shown that the extensions between two simpleprp^r-restrictedGG-modules coincide in all three categories provided the highest weights are “close" together.
Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula
Authors: Allouba Hassan
Published: September 2002

We delve deeper into our study of the connection of Brownian-time processes (BTPs) to fourth-order parabolic PDEs, which we introduced in a recent joint article with W. Zheng. Probabilistically, BTPs and their cousins BTPs with excursions form a unifying class of interesting stochastic processes that includes the celebrated IBM of Burdzy and other new intriguing processes and is also connected to the Markov snake of Le Gall. BTPs also offer a new connection of probability to PDEs that is fundamentally different from the Markovian one. They solve fourth-order PDEs in which the initial function plays an important role in the PDE itself, not only as initial data. We connect two such types of interesting and new PDEs to BTPs. The first is obtained by running the BTP and then integrating along its path, and the second type of PDEs is related to what we call the Feynman-Kac formula for BTPs. A special case of the second type is a step towards a probabilistic solution to linearized Cahn-Hilliard and Kuramoto-Sivashinsky type PDEs, which we tackle in an upcoming paper.
Kähler-Einstein metrics for some quasi-smooth log del Pezzo surfaces
Authors: Araujo Carolina
Published: September 2002

Recently Johnson and Kollár determined the complete list of anticanonically embedded quasi-smooth log del Pezzo surfaces in weighted projective

3
3

-spaces. They also proved that many of those surfaces admit a Kähler-Einstein metric, and that some of them do not have tigers. The aim of this paper is to settle the question of the existence of Kähler-Einstein metrics and tigers for those surfaces for which the question was left open. In order to do so, we will use techniques developed earlier by Nadel, Demailly and Kollár.
Two-weight norm inequalities for the Cesàro means of Hermite expansions
Authors: Muckenhoupt Benjamin , Webb David
Published: September 2002

An accurate estimate is obtained of the Cesàro kernel for Hermite expansions. This is used to prove two-weight norm inequalities for Cesàro means of Hermite polynomial series and for the supremum of these means. These extend known norm inequalities, even in the single power weight and “unweighted” cases. An almost everywhere convergence result is obtained as a corollary. It is also shown that the conditions used to prove norm boundedness of the means and most of the conditions used to prove the boundedness of the Cesàro supremum of the means are necessary.
Classification of compact complex homogeneous spaces with invariant volumes
Authors: Guan Daniel
Published: September 2002

We solve the problem of the classification of compact complex homogeneous spaces with invariant volumes (see Matsushima, 1961).
Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III
Authors: Tataru Daniel
Published: September 2002

In an earlier work of the author it was proved that the Strichartz estimates for second order hyperbolic operators hold in full if the coefficients are of class

C
2

C^2

. Here we strengthen this and show that the same holds if the coefficients have two derivatives in

L
1

(

L
∞

)

L^1(L^\infty )

. Then we use this result to improve the local theory for second order nonlinear hyperbolic equations.
Locally analytic distributions and 𝑝-adic representation theory, with applications to 𝐺𝐿₂
Authors: Schneider Peter , Teitelbaum Jeremy
Published: September 2002

In this paper we study continuous representations of locally

L
L

-analytic groups

G
G

in locally convex

K
K

-vector spaces, where

L
L

is a finite extension of

Q

p

\mathbb {Q}_p

and

K
K

is a spherically complete nonarchimedean extension field of

L
L

. The class of such representations includes both the smooth representations of Langlands theory and the finite dimensional algebraic representations of

G
G

, along with interesting new objects such as the action of

G
G

on global sections of equivariant vector bundles on

p
p

-adic symmetric spaces. We introduce a restricted category of such representations that we call “strongly admissible” and we show that, when

G
G

is compact, our category is anti-equivalent to a subcategory of the category of modules over the locally analytic distribution algebra of

G
G

. As an application we prove the topological irreducibility of generic members of the

p
p

-adic principal series for

G

L
2

(

Q

p

)

GL_2(\mathbb {Q}_p)

. Our hope is that our definition of strongly admissible representation may be used as a foundation for a general theory of continuous

K
K

-valued representations of locally

L
L

-analytic groups.
Multi-linear operators given by singular multipliers
Authors: Muscalu Camil , Tao Terence , Thiele Christoph
Published: September 2002

We prove

L
p

L^p

estimates for a large class of multi-linear operators, which includes the multi-linear paraproducts studied by Coifman and Meyer (1991), as well as the bilinear Hilbert transform and other operators with large groups of modulation symmetries.
Cluster algebras I: Foundations
Authors: Fomin Sergey , Zelevinsky Andrei
Published: September 2002

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
On the geometric Langlands conjecture
Authors: Frenkel E. , Gaitsgory D. , Vilonen K.
Published: September 2002

Let

X
X

be a smooth, complete, geometrically connected curve over a field of characteristic

p
p

. The geometric Langlands conjecture states that to each irreducible rank

n
n

local system

E
E

on

X
X

one can attach a perverse sheaf on the moduli stack of rank

n
n

bundles on

X
X

(irreducible on each connected component), which is a Hecke eigensheaf with respect to

E
E

. In this paper we derive the geometric Langlands conjecture from a certain vanishing conjecture. Furthermore, using recent results of Lafforgue, we prove this vanishing conjecture, and hence the geometric Langlands conjecture, in the case when the ground field is finite.
Noetherian hereditary abelian categories satisfying Serre duality
Authors: Reiten I. , Van den Bergh M.
Published: September 2002

In this paper we classify

Ext
\operatorname {Ext}

-finite noetherian hereditary abelian categories over an algebraically closed field

k
k

satisfying Serre duality in the sense of Bondal and Kapranov. As a consequence we obtain a classification of saturated noetherian hereditary abelian categories. As a side result we show that when our hereditary abelian categories have no non-zero projectives or injectives, then the Serre duality property is equivalent to the existence of almost split sequences.
Construction of discrete series for classical 𝑝-adic groups
Authors: Mœglin Colette , Tadić Marko
Published: September 2002

The classification of irreducible square integrable representations of classical

p
p

-adic groups is completed in this paper, under a natural local assumption. Further, this classification gives a parameterization of irreducible tempered representations of these groups. Therefore, it implies a classification of the non-unitary duals of these groups (modulo cuspidal data). The classification of irreducible square integrable representations is directly related to the parameterization of irreducible square integrable representations in terms of dual objects, which is predicted by Langlands program.
Supersingular elliptic curves, theta series and weight two modular forms
Authors: Emerton Matthew
Published: September 2002

Let

p
p

be a prime, and let

M

\mathcal {M}

denote the space of weight two modular forms on

Γ

0

(
p
)

\Gamma _{0}(p)

all of whose Fourier coefficients are integral, except possibly for the constant term, which should be either integral or half-integral. We prove that

M

\mathcal {M}

is spanned as a

Z

\mathbb {Z}

-module by theta series attached to the unique quaternion algebra that is ramified at

p
p

, at infinity, and at no other primes.
Growth of solutions for QG and 2D Euler equations
Authors: Cordoba Diego , Fefferman Charles
Published: September 2002

We study the rate of growth of sharp fronts of the Quasi-geostrophic equation and 2D incompressible Euler equations. The development of sharp fronts are due to a mechanism that piles up level sets very fast. Under a semi-uniform collapse, we obtain a lower bound on the minimum distance between the level sets.
The method of alternating projections and the method of subspace corrections in Hilbert space
Authors: Xu Jinchao , Zikatanov Ludmil
Published: September 2002

A new identity is given in this paper for estimating the norm of the product of nonexpansive operators in Hilbert space. This identity can be applied for the design and analysis of the method of alternating projections and the method of subspace corrections. The method of alternating projections is an iterative algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a finite number of subspaces by alternatively computing the best approximations from the individual subspaces which make up the intersection. The method of subspace corrections is an iterative algorithm for finding the solution of a linear equation in a Hilbert space by approximately solving equations restricted on a number of closed subspaces which make up the entire space. The new identity given in the paper provides a sharpest possible estimate for the rate of convergence of these algorithms. It is also proved in the paper that the method of alternating projections is essentially equivalent to the method of subspace corrections. Some simple examples of multigrid and domain decomposition methods are given to illustrate the application of the new identity.
Automorphisms of categories of free algebras of varieties
Authors: Mashevitzky G. , Plotkin B. , Plotkin E.
Published: September 2002

Let

Θ
\Theta

be an arbitrary variety of algebras and let

Θ
0

\Theta ^0

be the category of all free finitely generated algebras from

Θ
\Theta

. We study automorphisms of such categories for special

Θ
\Theta

. The cases of the varieties of all groups, all semigroups, all modules over a noetherian ring, all associative and commutative algebras over a field are completely investigated. The cases of associative and Lie algebras are also considered. This topic relates to algebraic geometry in arbitrary variety of algebras

Θ
\Theta

.
On the construction of a 𝐶²-counterexample to the Hamiltonian Seifert Conjecture in ℝ⁴
Authors: Ginzburg Viktor , Gürel Başak
Published: September 2002

We outline the construction of a properC2C^2-smooth function onR4\mathbb {R}^4such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as aC2C^2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.
Nonrational, nonsimple convex polytopes in symplectic geometry
Authors: Battaglia Fiammetta , Prato Elisa
Published: September 2002

In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e., the strata are locally modeled by

R

k

{\mathbb {R}}^k

modulo the action of a discrete, possibly infinite, group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back. These spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting. We provide here the explicit construction of these spaces, and a thorough description of the stratification.
Regular neighbourhoods and canonical decompositions for groups
Authors: Scott Peter , Swarup Gadde
Published: September 2002

We find canonical decompositions for finitely presented groups which essentially specialise to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under automorphisms of the group. A crucial new ingredient is the concept of a regular neighbourhood of a family of almost invariant subsets of a group. An almost invariant set is an analogue of an immersion.
Quantum affine algebras, combinatorics of Young walls, and global bases
Authors: Kang Seok-Jin , Kwon Jae-Hoon
Published: September 2002

We construct the Fock space representation of quantum affine algebras using combinatorics of Young walls. We also show that the crystal basis of the Fock space representation can be realized as the abstract crystal consisting of proper Young walls. We then generalize Lascoux-Leclerc-Thibon algorithm to obtain an effective algorithm for constructing the global bases of basic representations.
Twining Character Formula of Kac-Wakimoto Type for Affine Lie Algebras
Authors: Naito Satoshi
Published: September 2002

We prove a formula of Kac-Wakimoto type for the twining characters of irreducible highest weight modules of symmetric, noncritical, integrally dominant highest weights over affine Lie algebras. This formula describes the twining character in terms of the subgroup of the integral Weyl group consisting of elements which commute with the Dynkin diagram automorphism. The main tools in our proof are the (Jantzen) translation functor and the existence result of a certain local composition series which is stable under the Dynkin diagram automorphism.
Constructible characters, leading coefficients and left cells for finite Coxeter groups with unequal parameters
Authors: Geck Meinolf
Published: September 2002

Following Lusztig, we investigate constructible characters, leading coefficients and left cells for a finite Coxeter groupWWin the case of unequal parameters. We obtain explicit results forWWof typeF4F_4,BnB_nandI2(m)I_2(m)(mmeven) which support Lusztig’s conjecture that known results about left cells in the equal parameter case should remain valid in the case of unequal parameters.
Principal nilpotent orbits and reducible principal series
Authors: Kuo Wentang
Published: September 2002

Let

G
G

be a split reductive

p
p

-adic group. In this paper, we establish an explicit link between principal nilpotent orbits of

G
G

and the irreducible constituents of principal series of

G
G

. A geometric characterization of certain irreducible constituents is also provided.
Admissible nilpotent orbits of real and 𝑝-adic split exceptional groups
Authors: Nevins Monica
Published: September 2002

We determine the admissible nilpotent coadjoint orbits of real and

p
p

-adic split exceptional groups of types

G
2

G_2

,

F
4

F_4

,

E
6

E_6

and

E
7

E_7

. We find that all Lusztig-Spaltenstein special orbits are admissible. Moreover, there exist non-special admissible orbits, corresponding to “completely odd” orbits in Lusztig’s special pieces. In addition, we determine the number of, and representatives for, the non-even nilpotent

p
p

-adic rational orbits of

G
2

G_2

,

F
4

F_4

and

E
6

E_6

.
Representations of graded Hecke algebras
Authors: Kriloff Cathy , Ram Arun
Published: September 2002

Representations of affine and graded Hecke algebras associated to Weyl groups play an important role in the Langlands correspondence for the admissible representations of a reductive

p
p

-adic group. We work in the general setting of a graded Hecke algebra associated to any real reflection group with arbitrary parameters. In this setting we provide a classification of all irreducible representations of graded Hecke algebras associated to dihedral groups. Dimensions of generalized weight spaces, Langlands parameters, and a Springer-type correspondence are included in the classification. We also give an explicit construction of all irreducible calibrated representations (those possessing a simultaneous eigenbasis for the commutative subalgebra) of a general graded Hecke algebra. While most of the techniques used have appeared previously in various contexts, we include a complete and streamlined exposition of all necessary results, including the Langlands classification of irreducible representations and the irreducibility criterion for principal series representations.
Isogenies of Hecke algebras and a Langlands correspondence for ramified principal series representations
Authors: Reeder Mark
Published: September 2002

This paper gives a Langlands classification of constituents of ramified principal series representations for split

p
p

-adic groups with connected center.
Classification of unipotent representations of simple 𝑝-adic groups, II
Authors: Lusztig G.
Published: September 2002

Let

G

(

K

)

\mathbf G(\mathbf K)

be the group of

K

\mathbf K

-rational points of a connected adjoint simple algebraic group over a nonarchimedean local field

K

\mathbf K

. In this paper we classify the unipotent representations of

G

(

K

)

\mathbf G(\mathbf K)

in terms of the geometry of the Langlands dual group. This was known earlier in the special case where

G

(

K

)

\mathbf G(\mathbf K)

is an inner form of a split group.
Local systems on nilpotent orbits and weighted Dynkin diagrams
Authors: Achar Pramod , Sommers Eric
Published: September 2002

We study the Lusztig-Vogan bijection for the case of a local system. We compute the bijection explicitly in type A for a local system and then show that the dominant weights obtained for different local systems on the same orbit are related in a manner made precise in the paper. We also give a conjecture (putatively valid for all groups) detailing how the weighted Dynkin diagram for a nilpotent orbit in the dual Lie algebra should arise under the bijection.
On the failure of a generalized Denjoy-Wolff theorem
Authors: Poggi-Corradini Pietro
Published: September 2002

The classical Denjoy-Wolff Theorem for the unit disk was generalized, in 1988, by Maurice Heins, to domains bounded by finitely many analytic Jordan curves. Heins asked whether such an extension is valid more generally. We show that it can actually fail for some domains. Specifically, we produce an automorphism

ϕ
\phi

on a planar domain

Ω
\Omega

, such that the iterates of

ϕ
\phi

converge to a unique Euclidean boundary point, but do not converge to a unique Martin point in the Martin compactification of

Ω
\Omega

. We then extend this example to a family of examples in the second part of this work. We thus consider the Martin boundary for domains whose complement is contained in a strip and generalize results of Benedicks and Ancona.