on the polynomial solutions of the calogero sutherland moser model the symmetry of the polynomial solutions of the calogero sutherland moser model which corresponds to the deformed symmetric group or the general linear group gl n is treated using the relationship between and the unitary group su n a deformed relation su n is studied up to n 3

the schur rotation as a simple approach to the transition between quasiperiodic and periodic phases the recently observed transition of crnisi from the octahedral to a cubic phase has a natural mathematical counterpart in terms of a one parameter schur rotation the authors present the corresponding tilings and the diffraction patterns of delta scatterers at vertex positions for a series of rotation angles these angles show up as a length scaling in the patterns and provide a measurable order parameter they comment on the rational reductions and give two further examples one on a connection between octagonal and dodecagonal patterns and one on a transition between icosahedral and primitive or body centred cubic phases

structure and representations of the hyperoctahedral group in this paper the main properties of the symmetry group of the n dimensional cube are reviewed and formulated with respect to possible applications in lattice theories the connection between the hyperoctahedral group wn and the orthogonal group o n is investigated by means of the canonical representation

the l s coupling revisited a general solution for the 4 electron system the relation between the unitary group su n and the symmetric group sn is treated using the induced characters of sn by means of this approach the l s coupling for four electrons is solved

global analysis for strong solutions to the equations of a ferrofluid flow model national science foundation of china 10531020 national natural science foundation of china nsaf 10976026

branching rules for the hyperoctahedral group reduction theorems for the decomposition of induced and irreducible characters of w bn in terms of induced and irreducible characters of w bn 1 respectively are given

cycle integrals of the j function and mock modular forms in this paper we construct certain mock modular forms of weight 1 2 whose fourier coecients are given in terms of cycle integrals of the modular j function their shadows are weakly holomorphic forms of weight 3 2 these new mock modular forms occur as holomorphic parts of weakly harmonic maass forms we also construct a generalized mock modular form of weight 1 2 having a real quadratic class number times a regulator as a fourier coecient as an application of these forms we study holomorphic modular integrals of weight 2 whose rational period functions have poles at certain real quadratic integers the fourier coecients of these modular integrals are given in terms of cycle integrals of modular functions such a modular integral can be interpreted in terms of a shimura type lift of a mock modular form of weight 1 2 and yields a real quadratic analogue of a borcherds product

branching rules for the weyl group w dn reduction theorems for the decomposition of induced and irreducible characters of w dn in terms of induced and irreducible characters of w dn 1 respectively are given

strong solutions to the equations of a ferrofluid flow model abstract we study the differential system introduced by m i shliomis to describe the motion of a ferrofluid driven by an external magnetic field the system is a combination of the navier stokes equations the magnetization equation and the magnetostatic equations no regularizing term is added to the magnetization equation we prove the local in time existence of strong solutions to the system

symmorphic space groups of finite crystal lattices the symmorphic space group of a finite n dimensional crystal lattice is studied and its factorization is presented this lattice is determined by a direct product of cyclic groups and then its translation point and space groups are defined as modular images of corresponding ones for a lattice of infinite extent a factorization of holohedries of an infinite lattice is used in order to present a symmorphic finite space group as a direct product as an example and as a very special case a space group in the case of the hypercubic lattice is studied and its irreducible representations are investigated the results obtained suggest that for vectors lying on a surface of the first brillouin zone i e for which at least one coordinate is equal to 0 or 1 2 an additional index describing their symmetry properties should be introduced this enables the authors to make a more detailed classification of states energy levels on the other hand finite symmorphic space groups can be used within e g the so called finite lattice approach

hilbert class polynomials and traces of singular moduli where q e the values of j z at imaginary quadratic arguments in the upper half of the complex plane are known as singular moduli singular moduli are algebraic integers which play prominent roles in classical and modern number theory see c bcsh for example hilbert class fields of imaginary quadratic fields are generated by singular moduli furthermore isomorphism classes of elliptic curves with complex multiplication are distinguished by singular moduli throughout let d 0 3 mod 4 be a positive integer so that d is the discriminant of an order in an imaginary quadratic field and let h d be the hurwitz kronecker class number for the discriminant d let qd be the set of positive definite integral binary quadratic forms note including imprimitive forms if there are any

coefficient of maass forms and the siegel zero with an appendix by dorian goldfeld jeffrey hoffstein and daniel lieman

on the relations between irreducible representations of the hyperoctahedral group and o 4 and so 4 in this paper we describe the relations between the irreducible representations of the hyperoctahedral group in four dimensions and irreducible low dimensional representations of the orthogonal groups o 4 and so 4

the large n limit of the discrete cubic and chiral cubic models the mean field theory of the discrete cubic and chiral cubic systems is shown to be exact in the n to infinity limit

the unique labelling of states via mackey s theorem a new approach to finding unique labels for many electron states in multicentre systems is described and a particular example eight electrons in s states on eight centres is worked out in detail this approach is shown to provide a labelling with a more direct physical interpretation than has previously been found

stability and uniqueness of magnetic fluid motions we examine the uniqueness and asymptotic stability of the equilibrium and arbitrary flows for a general class of the governing equations for magnetic fluids stability bounds for equilibrium base flows in mechanically isolated domains are obtained and it is shown that in general these are asymptotically stable for general non trivial flows we obtain stability bounds and establish uniqueness theorems for the initial boundary value problems of magnetic fluids

structure and representations of the symmetry group of the four dimensional cube in this paper we give explicitly the description of the structure the characters and the complete system of irreducible representations of the hyperoctahedral group in four dimensions which we call w4 from the german wurfel in a second step we do the same for the subgroup sw4 which is formed by all pure rotations contained in w4

hybrid bounds for twisted l functions the aim of this paper is to derive bounds on the critical line s 1 for l functions attached to twists f of a primitive cusp form f of level n and a primitive character modulo q that break convexity simultaneously in the s and q aspects if f has trivial nebentypus it is shown that

on the symmetry of logic embedding logical operations in non dissipative physical processes requires the use of reversible logic following feynman s 1986 approach the sixteen distinct truth tables of classical logic are shown to be contained in the 8 reversible logic operations covered by the symmetric group s8 which permute the eight values of three logical variables small subgroups of s8 are shown to cover respectively reversible logic reversible switching and reversible arithmetic a new universal primitive is found which generates a covering group of reversible logic it is shown that the octahedral group in four dimensions covers both reversible logic and switching and hence that the orthogonal group o 4 provides a covering group for quantum gates

the 192 solutions of the heun equation a machine generated list of 192 local solutions of the heun equation is given they are analogous to kummer s 24 solutions of the gauss hypergeometric equation since the two equations are canonical fuchsian differential equations on the riemann sphere with four and three singular points respectively tabulation is facilitated by the identification of the automorphism group of the equation with n singular points as the coxeter group d n each of the 192 expressions is labeled by an element of d 4 of the 192 24 are equivalent expressions for the local heun function hl and it is shown that the resulting order 24 group of transformations of hl is isomorphic to the symmetric group s 4 the isomorphism encodes each transformation as a permutation of an abstract four element set not identical to the set of singular points

values of modular functions at real quadratics and conjectures of kaneko in 2008 kaneko made several interesting observations about the values of the modular j invariant at real quadratic irrationalities the values of modular functions at real quadratics are defined in terms of their cycle integrals along the associated geodesics in this paper we prove some of the conjectures of kaneko for a general modular function

the global symmetries of spin systems defined on abelian groups ii we consider the classification problem of the global symmetry groups of spin systems defined on abelian groups its implications on the generating functional the transfer matrix the hamiltonian formalism and factorization properties of spin systems are discussed the duality properties of spin systems defined on semidirect products of abelian groups are revisited in the first of this series of three papers we list the groups for systems defined on zp p prime z2 z2 and z2 z2 z2 manifolds they are direct or wreath products of m metacyclic groups and symmetric groups

modular functions and the uniform distribution of cm points 1 zd i d 2 if d 0 mod 4 1 i d 2 if d 3 mod 4 the j function has the remarkable property that j zd is an algebraic integer of degree h d the class number of k q zd in fact k j zd is the hilbert class field of k 4 the first few values of j zd are j z3 0 j z4 12 j z7 153 j z8 20 j z11 323 j z15 191025 85995 5 2 j z19 963 j z20 632000 282880 5