We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the Sn-irreducible representation indexed by the staircase partition contains every irreducible representation of Sn. We present a sufficient condition allowing to determine whether an irreducible representation is...

This paper shows that for a given irreducible representation ρ of Γ/Γ1, the two functions dim(Mk(Γ1, ρ)) and dim(Sk(Γ1, ρ)) of k are almost linear functions. Let Γ and Γ1 be two Fuchsian subgroups of SL2(Q) of the first kind, with Γ1 a normal subgroup of Γ of index μ. Let H denote the extended upper half-plane [4] and put Y = Γ\H and X = Γ1\H . Let Ak(∗) denotes the space of meromorphic modular...

Founding harmonic analysis on classical simple complex groups, I.M. Gelfand and M.A. Naimark in their classical book [GN] posed three basic questions: unitary duals, characters of irreducible unitary representations and Plancherel measures. In the case of reductive p-adic groups, the only series of reductive groups where unitary duals are known are general linear groups. In this paper we reduce...

Let V be a symplectic vector space of dimension 2n. Given a partition λ with at most n parts, there is an associated irreducible representation S[λ](V ) of Sp(V ). This representation admits a resolution by a natural complex L• , which we call the Littlewood complex, whose terms are restrictions of representations of GL(V ). When λ has more than n parts, the representation S[λ](V ) is not defin...

In this article, we describe the Schur multiplier and representation group of discrete Heisenberg groups their t-variants. We give a construction all complex finite-dimensional irreducible projective representations these groups.

Consider real reductive group G, as defined in [Wal88]. Let Π be an irreducible admissible representation of G with the distribution character ΘΠ, [Har51]. Denote by uΠ the lowest term in the asymptotic expansion of ΘΠ, [BV80]. This is a finite linear combination of Fourier transforms of nilpotent coadjoint orbits, uΠ = ∑ O cOμ̂O. As shown by Rossmann, [Ros95], the closure of the union of the ni...

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs discretely with finite multiplicity (admissible restrictions). Basic theory and new perspectives of admissible restrictions are presented from both analytic and alge...

Let G be a simply connected Chevalley group over a p-adic field, with the residue field of order q, corresponding to an irreducible simply laced root system. We show that the minimal representation V of G can be defined over Q. We show that the reduction of V modulo l 6= p is minimal (in appropriate sense) and is irreducible for l outside an explicit, finite set determined by q.

We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible corre...