measuring inconsistency in probabilistic logic consistency independence and continuity are incompatible postulates minimal inconsistent sets are not suitable to analyze probabilistic incon sistencies independence can be weakened considering the underlying consolidation process inconsistency and incoherence measures based on distances and dutch books coincide inconsistency measures have been proposed as a way to manage inconsistent knowledge bases in the ai community to deal with inconsistencies in the context of conditional probabilistic logics rationality postulates and computational efficiency have driven the formulation of inconsistency measures independently investigations in formal epistemol ogy have used the betting concept of dutch book to measure an agent s degree of incoherence in this paper we show the impossibility of joint satisfiability of the proposed postulates proposing to replace them by more suitable ones thus we reconcile the rationality postulates for inconsistency measures in probabilistic bases and show that several inconsistency measures suggested in the literature and computable with linear programs satisfy the reconciled postulates additionally we give an interpretation for these feasible measures based on the formal epistemology concept of dutch book bridging the views of two so far separate communities in ai and philosophy in particular we show that incoherence degrees in formal epistemology may lead to novel approaches to inconsistency measures in the ai view

abelianisation of orthogonal groups and the fundamental group of modular varieties abstract we study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms we show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry in particular the moduli of k3 surfaces we give applications to modular forms and to computing the fundamental groups of some moduli spaces

on the genericity of cuspidal automorphic forms of so2n 1 this is a sequel of our work js06 we extend moeglin s results m97a and m97b from the even orthogonal groups to old orthogonal groups and complete our proof of the cap conjecture for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models we also give characterization of the vanishing of the central value of the standard l function of so2n 1 a in terms of theta correspondence as result we obtain the weak langlands functorial transfer from so2n 1 a to gl2n a for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

a frequency domain approach to control of singular systems in this paper singular control systems are studied from the frequency domain point of view the proper stable factorization of a singular system is derived the stability of the closed loop system consisting of a singular system and controller is addressed most significantly all proper stabilizing controllers are parameterized for a given singular system

anytime deduction for probabilistic logic abstract this paper proposes and investigates an approach to deduction in probabilistic logic using as its medium a language that generalizes the propositional version of nilsson s probabilistic logic by incorporating conditional probabilities unlike many other approaches to deduction in probabilistic logic this approach is based on inference rules and therefore can produce proofs to explain how conclusions are drawn we show how these rules can be incorporated into an anytime deduction procedure that proceeds by computing increasingly narrow probability intervals that contain the tightest entailed probability interval since the procedure can be stopped at any time to yield partial information concerning the probability range of any entailed sentence one can make a tradeoff between precision and computation time the deduction method presented here contrasts with other methods whose ability to perform logical reasoning is either limited or requires finding all truth assignments consistent with the given sentences

on automorphisms of enriques surfaces an enriques surface over an algebraically closed field k of characteristic 4 2 is a nonsingular projective surface f with hi f gv h2 f or 0 2kv 0 the unramified double cover of f defined by the torsion class k v is a k3 surface f a nonsingular projective surface with hi f gr 0 kr 0 the study of enriques surfaces is equivalent to the study of k3 surfaces with a fixed point free involution z in particular the automor phism group aut f of f is isomorphic to the group aut ff z z where aut f z is the centralizer of z in the automorphism group aut f of ft in the case k the field of complex numbers the study of aut f is based on the global torelli theorem for k3 surfaces proven by i piatetski shapiro and i shafarevich in 19 it follows from this theorem that up to a finite group the group aut ff is isomorphic to the quotient group o pic f w where o pic f is the orthogonal group of the picard lattice of ff and w its normal subgroup generated by the reflections into the classes of nonsingular rational curves for a generic enriques surface f this theorem allows to compute aut f see 3 and also 17 where this result is not stated explicitly for an arbitrary f the relation between f and ff does not help since it is very difficult to compute the action of z in pie if however by other means we can prove the following analog of piatetski shapiro and shafarevich s result

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

moduli spaces of polarized symplectic o grady varieties and borcherds products we study moduli spaces of o grady s ten dimensional irreducible symplectic manifolds these moduli spaces are covers of modular varieties of dimension 21 namely quotients of hermitian symmetric domains by a suitable arithmetic group the interesting and new aspect of this case is that the group in question is strictly bigger than the stable orthogonal group this makes it different from both the k3 and the k3 n case which are of dimension 19 and 20 respectively

technical communique all doubly coprime factorizations of a general rational matrix for a general rational matrix function possibly polynomial or improper we give state space formulas for the class of all doubly coprime factorizations over an arbitrary fixed set in the closed complex plane the main result is expressed in terms of a special type of realization called centered that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the proper case in particular the formulas can be specialized to get the parametrization of all proper polynomial or proper and stable doubly coprime factorizations of an arbitrary descriptor system en route we provide a closed state space formula for the inverse of an invertible general rational matrix

a theory of diagnosis from first principles suppose one is given a description of a system together with an observation of the system s behaviour which conflicts with the way the system is meant to behave the diagnostic problem is to determine those components of the system which when assumed to be functioning abnormally will explain the discrepancy between the observed and correct system behaviour we propose a general theory for this problem the theory requires only that the system be described in a suitable logic moreover there are many such suitable logics e g first order temporal dynamic etc as a result the theory accommodates diagnostic reasoning in a wide variety of practical settings including digital and analogue circuits medicine and database updates the theory leads to an algorithm for computing all diagnoses and to various results concerning principles of measurement for discriminating among competing diagnoses finally the theory reveals close connections between diagnostic reasoning and nonmonotonic reasoning

on the noether lefschetz theorem and some remarks on codimension two cycles here of general moduli means that there is a countable union v of subvarieties of the space pn of surfaces of degree d in p3 such that the statement pie s z holds for s p n v noether it would seem stated this theorem but never completely proved it instead he gave a plausibility argument based on the following construction 1 let g be the hilbert scheme of curves of degree n and genus 9 in p3 l gr3 d l ip n the space of surfaces of degree d in p3 and zc t the incidence correspondence s o a c s c z s

localising iceberg inconsistencies in artificial intelligence it is important to handle and analyse inconsistency in knowledge bases inconsistent pieces of information suggest questions like where is the inconsistency and how severe is it inconsistency measures have been proposed to tackle the latter issue but the former seems underdeveloped and is the focus of this paper minimal inconsistent sets have been the main tool to localise inconsistency but we argue that they are like the exposed part of an iceberg failing to capture contradictions hidden under the water using classical propositional logic we develop methods to characterise when a formula is contributing to the inconsistency in a knowledge base and when a set of formulas can be regarded as a primitive conflict to achieve this we employ an abstract consequence operation to look beneath the water level generalising the minimal inconsistent set concept and the related free formula notion we apply the framework presented to the problem of measuring inconsistency in knowledge bases putting forward relaxed forms for two debatable postulates for inconsistency measures finally we discuss the computational complexity issues related to the introduced concepts

pole placement and compensator design of generalized systems abstract the system considered is a generalized system e ax bu y cx with matrix e singular when the impulsive modes of the system are both controllable and observable it is shown in this paper that these modes can be eliminated by almost any constant output feedback for a strongly controllable and observable generalized system after its impulsive modes are eliminated the poles of the system can be assigned arbitrarily by state feedback even if the states are not available the paper adopts an efficient method to design a compensator for the system

parametrization of ω stabilizing controllers and closed loop transfer matrices of a singular system abstract for a completely general singular system whose transfer matrix may be improper or even polynomial and an arbitrary set in the closed complex plane we give a state space parametrization of all controllers that achieve closed loop transfer matrices having all poles in and of the respective closed loop transfer matrices the main result is expressed in terms of a special type of state space realization called centered that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the standard proper case in particular the formulas can be specialized to get the parametrization of all controllers that achieve proper polynomial or proper and stable closed loop transfer matrices for a singular system

on the kodaira dimension of orthogonal modular varieties we prove that up to scaling there are only finitely many integral lattices l of signature 2 n with n ge 21 or n 17 such that the modular variety defined by the orthogonal group of l is not of general type in particular when n ge 108 every modular variety defined by an arithmetic group for a rational quadratic form of signature 2 n is of general type we also obtain similar finiteness in n ge 9 for the stable orthogonal groups as a byproduct we derive finiteness of lattices admitting reflective modular form of bounded vanishing order which proves a conjecture of gritsenko and nikulin

brief bezout identity related to reduced order observer based controllers for singular systems a design method of causal reduced order observer based controllers for singular systems is presented a new state space representation of the bezout identity for singular systems is developed a parameterization of all causal reduced order controllers is also given the general results given here can be extended to various cases including minimal and full order observer based controllers

k3 surfaces with involution equivariant analytic torsion and automorphic forms on the moduli space in this paper we introduce an invariant of a k3 surface with 2 action equipped with a 2 invariant kahler metric which we obtain using the equivariant analytic torsion of the trivial line bundle this invariant is shown to be independent of the choice of the kahler metric it can be viewed as a function on the moduli space of k3 surfaces with involution the main result of this paper is that this function can be identified with an automorphic form which characterizes the discriminant locus in particular we show that the ray singer analytic torsion of the trivial line bundle on an enriques surface with ricci flat kahler metric is given by the value of the norm of the borcherds function at its period point

inconsistency measures for probabilistic logics inconsistencies in knowledge bases are of major concern in knowledge representation and reasoning in formalisms that employ model based reasoning mechanisms inconsistencies render a knowledge base useless due to the non existence of a model in order to restore consistency an analysis and understanding of inconsistencies are mandatory recently the field of inconsistency measurement has gained some attention for knowledge representation formalisms based on classical logic an inconsistency measure is a tool that helps the knowledge engineer in obtaining insights into inconsistencies by assessing their severity in this paper we investigate inconsistency measurement in probabilistic conditional logic a logic that incorporates uncertainty and focuses on the role of conditionals i e if then rules we do so by extending inconsistency measures for classical logic to the probabilistic setting further we propose novel inconsistency measures that are specifically tailored for the probabilistic case these novel measures use distance measures to assess the distance of a knowledge base to a consistent one and therefore takes the crucial role of probabilities into account we analyze the properties of the discussed measures and compare them using a series of rationality postulates

on the measure of conflicts shapley inconsistency values there are relatively few proposals for inconsistency measures for propositional belief bases however inconsistency measures are potentially as important as information measures for artificial intelligence and more generally for computer science in particular they can be useful to define various operators for belief revision belief merging and negotiation the measures that have been proposed so far can be split into two classes the first class of measures takes into account the number of formulae required to produce an inconsistency the more formulae required to produce an inconsistency the less inconsistent the base the second class takes into account the proportion of the language that is affected by the inconsistency the more propositional variables affected the more inconsistent the base both approaches are sensible but there is no proposal for combining them we address this need in this paper our proposal takes into account both the number of variables affected by the inconsistency and the distribution of the inconsistency among the formulae of the base our idea is to use existing inconsistency measures in order to define a game in coalitional form and then to use the shapley value to obtain an inconsistency measure that indicates the responsibility contribution of each formula to the overall inconsistency in the base this allows us to provide a more reliable image of the belief base and of the inconsistency in it

conditional logic and the principle of entropy abstract the conditional three valued logic of calabrese is applied to the language l of conditionals on propositional variables with finite domain the conditionals in l serve as a means for the construction and manipulation of probability distributions respecting the principle of maximum entropy and of minimum relative entropy this principle allows a sound inference even in the presence of uncertain evidence the inference is directed it respects a probabilistic version of modus ponens not of modus tollens it permits transitive chaining and supports a cautious monotony conjunctive conditional and material deduction are manageable in this probabilistic logic too the concept is not merely theoretical but enables large scale applications in the expert system shell spirit

enriques surfaces analytic discriminants and borcherds s φ function in bor 96 borcherds constructed a non vanishing weight 4 modular form on the moduli space of marked polarized enriques surface of degree 2 by considering the twisted denominator function of the fake monster lie algebra associated to an automorphism of order 2 of the leech lattice fixing an 8 dimensional subspace in jt 94 and jt 96 we defined and studied a meromorphic multi valued modular form of weight 2 which we call the k3 analytic discriminant on the moduli space of marked polarized k3 surfaces of degree 2d in certain cases including when where p k are distinct primes our meromorphic form is actually a holomorphic form our construction involves a determinant of the laplacian on a polarized k3 surface with respect to the calabi yau metric together with the l 2 norm of the image of the period map with respect to a properly scaled holomorphic two form since the universal cover of any enriques surface is a k3 surface we can restrict the k3 analytic discriminant to the moduli space of degree 2 enriques surfaces the main result of this paper is the observation that the square of our degree 2 analytic discriminant viewed as a function on the moduli space of degree 2 enriques surfaces is equal to the borcherd s function up to a universal multiplicative constant this result generalizes known results in the study of generalized kac moody algebras and elliptic curves and suggests further connections with higher dimensional calabi yau varieties specifically those which can be realized as complete intersections in some possibly weighted projective space

technical communique doubly coprime factorizations related to any stabilizing controllers in state space given a plant and an arbitrary stabilizing controller we present state space formulas for doubly coprime factorizations related to the given controller then we determine parametrizations of all stabilizing controllers centered on that controller

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

the weil petersson geometry of the moduli space of su n 3 calabi yau manifolds i the weil petersson metric is defined on the moduli space of calabi yau manifolds the curvature of this weil petersson metrics is computed and its potential is explicitely defined it is proved that the moduli space of calabi yau manifolds is unobstructed see tian

the kodaira dimension of the moduli of k3 surfaces the global torelli theorem for projective k3 surfaces was first proved by piatetskii shapiro and shafarevich 35 years ago opening the way to treating moduli problems for k3 surfaces the moduli space of polarised k3 surfaces of degree 2d is a quasi projective variety of dimension 19 for general d very little has been known hitherto about the kodaira dimension of these varieties in this paper we present an almost complete solution to this problem our main result says that this moduli space is of general type for d 61 and for d 46 50 54 57 58 60

transcending classical invariant theory let sp2 r sp2 sp be the real symplectic group of rank n let sp denote the two fold cover of sp there is a unitary representation constructed by shale sh and weil wa of sp that is of considerable interest in the theory of automorphic forms we denote this representation by co and call it the oscillator representation the purpose of this paper is to establish about c a fact that should be useful for clarifying the structure of spaces of automorphic forms constructed using co we begin by formulating the result let e be a reductive subgroup of sp and let e denote the inverse image of e in sp denote by r e the set of infinitesimal equivalence classes of continuous irreducible admissible representations of e on locally convex spaces let co be the smooth representation of sp associated to co let co be realized on a hilbert space and let the subspace of smooth vectors on which space co is defined be written denote by r9 e co the set of elements of e which are realized as quotients by co e invariant closed subspaces of t g consider a reductive dual pair g g c sp h2 it is not hard to show that g and g commute with one another hence we may regard co i g g as a representation of gx g it is well known f that r gx g s9 g xr9 g the identification associates to p e r g and p e i g the tensor product p x p we note that p x p is not defined as a topological vector space nevertheless the infinitesimal equivalence class of p op is well defined select p x p e g x g suppose that in fact p p e 9 g g c then clearly p e r g c and p e 9 g c hence g co defines the graph of a correspondence between certain subsets of r9 g cv and j g co in fact the situation is quite precise

non symplectic involutions of irreducible symplectic manifolds of k3 n type this paper is concerned with non symplectic involutions of irreducible symplectic manifolds of k3 n type we will give a criterion for deformation equivalence and use this to give a lattice theoretic description of all deformation types while moduli spaces of k3 n type manifolds with non symplectic involutions are not necessarily hausdorff we will construct quasi projective moduli spaces for a certain well behaved class of such pairs

a general doubly coprime factorization for descriptor systems doubly coprime factorization plays an important role in dealing with multivariable control problems using a factorization approach in this study based on an arbitrary and properly stabilizing controller a general formula of doubly coprime factorization is obtained for use in descriptor systems detailed results have been derived on bridging the factorization approaches previously available in the literature

the tate conjecture for k3 surfaces in odd characteristic we show that the classical kuga satake construction gives rise away from characteristic 2 to an open immersion from the moduli of primitively polarized k3 surfaces of any fixed degree to a certain regular integral model for a shimura variety of orthogonal type this allows us to attach to every polarized k3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety in turn this reduces the tate conjecture for k3 surfaces over finitely generated fields of odd characteristic to a version of the tate conjecture for certain endomorphisms on the attached kuga satake abelian variety which we prove as a by product of our methods we also show that the moduli stack of primitively polarized k3 surfaces of degree 2d is quasi projective and when d is not divisible by p 2 is geometrically irreducible in characteristic p we indicate how the same method applies to prove the tate conjecture for co dimension 2 cycles on cubic fourfolds

doubly coprime matrix fraction representations using proportional and derivative feedback concepts in generalized state space systems the concepts of proportional and derivative state feedback are used to derive some explicit formulas for doubly coprime matrix fraction representations of generalized state space systems specifically proportional and derivative state feedback is used to determine the doubly coprime matrix fraction representations and to solve the corresponding generalized bezout identity in polynomial matrix form

mapping class group and a global torelli theorem for hyperkahler manifolds a mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies we compute a mapping class group of a hyperkahler manifold m showing that it is commensurable to an arithmetic lattice in so 3 b2 3 a teichmuller space of m is a space of complex structures on m up to isotopies we define a birational teichmuller space by identifying certain points corresponding to bimeromorphically equivalent manifolds we show that the period map gives the isomorphism between connected components of the birational teichmuller space and the corresponding period space so b2 3 3 so 2 so b2 3 1 we use this result to obtain a torelli theorem identifying each connected component of the birational moduli space with a quotient of a period space by an arithmetic group when m is a hilbert scheme of n points on a k3 surface with n 1 a prime power our torelli theorem implies the usual hodge theoretic birational torelli theorem for other examples of hyperkahler manifolds the hodge theoretic torelli theorem is known to be false

on the moduli space of pairs consisting of a cubic threefold and a hyperplane abstract we study the moduli space of pairs x h consisting of a cubic threefold x and a hyperplane h in p 4 the interest in this moduli comes from two sources the study of certain weighted hypersurfaces whose middle cohomology admit hodge structures of k3 type and on the other hand the study of the singularity o 16 the cone over a cubic surface in this paper we give a hodge theoretic construction of the moduli space of cubic pairs by relating x h to certain lattice polarized cubic fourfolds y a period map for the pairs x h is then defined using the periods of the cubic fourfolds y the main result is that the period map induces an isomorphism between a git model for the pairs x h and the baily borel compactification of some locally symmetric domain of type iv

cycles with local coefficients for orthogonal groups and vector valued siegel modular forms the purpose of this paper is to generalize the relation between intersection numbers of cycles in locally symmetric spaces of orthogonal type and fourier coefficients of siegel modular forms to the case where the cycles have local coefficients now the correspondence will involve vector valued siegel modular forms

on the converse theorem for borcherds products abstract we prove a new converse theorem for borcherds multiplicative theta lift which improves the previously known results to this end we develop a newform theory for vector valued modular forms for the weil representation which might be of independent interest we also derive lower bounds for the ranks of the picard groups and the spaces of holomorphic top degree differential forms of modular varieties associated to orthogonal groups

moduli spaces of twisted k3 surfaces and cubic fourfolds motivated by the relation between twisted k3 surfaces and special cubic fourfolds we construct moduli spaces of polarized twisted k3 surfaces of any fixed degree and order we do this by mimicking the construction of the moduli space of untwisted polarized k3 surfaces as a quotient of a bounded symmetric domain

l2 cohomology of arithmetic varieties abstract the l2 cohomology of arithmetic quotients of bounded symmetric domains is studied we establish the conjecture of zucker equating the l2 cohomology of these spaces to the intersection cohomology of their baily borel compactifications

the hodge conjecture and arithmetic quotients of complex balls let s be a closed shimura variety uniformized by the complex n ball associated with a standard unitary group the hodge conjecture predicts that every hodge class in h 2k s mathbb q k 0 dots n is algebraic we show that this holds for all degrees k away from the neighborhood bigl tfrac13n tfrac23n bigr of the middle degree we also prove the tate conjecture for the same degrees as the hodge conjecture and the generalized form of the hodge conjecture in degrees away from an interval depending on the codimension c of the subvariety centered at the middle dimension of s these results are derived from a general theorem that applies to all shimura varieties associated with standard unitary groups of any signature the proofs make use of arthur s endoscopic classification of automorphic representations of classical groups as such our results rely on the stabilization of the trace formula for the disconnected groups gl n rtimes langle theta rangle associated with base change

picard number of the generic fiber of an abelian fibered hyperkahler manifold we shall show that the picard number of the generic fiber of an abelian fibered hyperkahler manifold over the projective space is always one we then give a few applications for the mordell weil group in particular by deforming o grady s 10 dimensional manifold we construct an abelian fibered hyperkahler manifold of mordell weil rank 20 which is the maximum possible among all known ones

periods of double epw sextics we study the period map for double epw sextics which are varieties making up a locally versal family of polarized hyperkahler fourfolds double epw sextics are parametrized by lagrangian subspaces of the third wedge product of a 6 dimensional complex vector space we prove that lagrangians in the indeterminacy locus of the period map contain a decomposable 3 vector enjoying very special properties in addition we prove a result about periods of double epw sextics which are either smooth or have isolated singular points with projectivized tangent cone isomorphic to the incidence variety in mathbb p 2 times mathbb p 2 vee

doubly coprime fractional representations of generalized dynamical systems explicit formulas for doubly coprime fractional representations of the transfer matrix of a generalized dynamical system are given in terms of a stabilizable and detectable state space realization of the transfer matrix these formulas establish a possible way to use the fractional representation approach in the synthesis of generalized dynamical systems

the noether lefschetz conjecture and generalizations we prove the noether lefschetz conjecture on the moduli space of quasi polarized k3 surfaces this is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles i e sub arithmetic manifolds of the same type for compact manifolds this was proved in 3 here we extend the results of 3 to non compact manifolds this allows us to apply our results to the moduli spaces of quasi polarized k3 surfaces

abelian quotients of mapping class groups of highly connected manifolds we compute the abelianisations of the mapping class groups of the manifolds w g 2n g s n times s n for n ge 3 and g ge 5 the answer is a direct sum of two parts the first part arises from the action of the mapping class group on the middle homology and takes values in the abelianisation of the automorphism group of the middle homology the second part arises from bordism classes of mapping tori and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable j homomorphism we relate its calculation to a purely homotopy theoretic problem

twisted endoscopy and reducibility of induced representations for p adic groups 1 introduction this is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the levi factors ofmaximal parabolic subgroups of p adic groups on the unitary axis the problem is equivalent to determining certain local langlands l functions which are of arithmetic significance by themselves one of the main aims of this paper is to interpret our results in the direction of the parametrization problem by means of the theory of twisted endoscopy for which our method seems to be very suitable when the representation is supercuspidal we also study the reducibility of the induced representations off the unitary axis let f be a p adic field of characteristic zero fix a positive integer n 1 and let g be either of the groups sp2n s02n or s02n l in all three cases there is a conjugacy class of maximal parabolic subgroups which has gl as its levi factor let p mn be the standard parabolic subgroup ofg in this conjugacy class then m gl let tr be a discrete series representation of m gln f and given s c let i s tr be the representation of g g f induced from tr r idet ls let i tr i 0 tr

le lemme fondamental pondere ii enonces cohomologiques dans cet article on etudie la cohomologie de la fibration de hitchin tronquee introduite dans un article precedent on etend les principaux theoremes de ngo sur la cohomologie de la partie elliptique de la fibration de hitchin comme consequence on obtient une demonstration du lemme fondamental pondere d arthur in this paper we study the cohomology of the truncated hitchin fibration which was introduced in a previous paper we extend ngo s main theorems on the cohomology of the elliptic part of the hitchin fibration as a consequence we get a proof of arthur s weighted fundamental lemma

doubly coprime factorizations reduced order observers and dynamic state estimate feedback doubly coprime factorizations of the transfer function of a lumped linear time invariant system are a starting point for many of the results in the factorization approach to multivariabie control system analysis and synthesis in work by nett et al 1984 explicit state space realizations of these factorizations are derived using results from state estimation state feedback theory here new doubly coprime factorizations are developed based on minimal order observers following on from this various extensions are noted and it is proved that the class of all proper stabilizing controllers for a given plant can be generated by dynamic feedback of the reduced order state estimate