Abstract. We study spherical Whittaker functions on a metaplectic cover of GL(r + 1) over a nonarchimedean local field using lattice models from statistical mechanics. An explicit description of this Whittaker function was given in terms of Gelfand-Tsetlin patterns in [5, 17], and we translate this description into an expression of the values of the Whittaker function as partition functions of ...

We prove, using a technique developed for GL(n) in Howe and Moy H], a bijection between generalized Hecke algebras of G = SL(2; F) over a p-adic eld and those of its n-fold metaplectic cover G. This result implies that there is a canonical correspondence between irreducible admissible representations of G and genuine irreducible admissible representations of G of \suuciently large level" (depen...

and the Whittaker models of the inducing representation π M (cf. Theorem 2 of [4]). In this paper, Rodier’s theorem on the “heredity” of Whittaker models is extended to the non-algebraic setting of the n-fold metaplectic cover G̃ of G, where n is a positive integer such that F contains all of the n-th roots of unity. The main result is stated as a theorem in §2. In order to illustrate the situat...

We study spherical Whittaker functions on a metaplectic cover of GL(r + 1) over a nonarchimedean local field using lattice models from statistical mechanics. An explicit description of this Whittaker function was given in terms of Gelfand-Tsetlin patterns in [5, 17], and we translate this description into an expression of the values of the Whittaker function as partition functions of a sixverte...

Suppose that G and H are connected reductive groups over a number field F and that an L-homomorphism ρ : LG −→ LH is given. The Langlands functoriality conjecture predicts the existence of a map from the automorphic representations of G(A) to those of H(A). If the adelic points of the algebraic groups G, H are replaced by their metaplectic covers, one may hope to specify an analogue of the Lgro...

Abstract A general Voronoï summation formula for the (metaplectic) double cover of $\operatorname{GL}_2$ is derived via representation theoretic framework à la Ichino–Templier. The identity also formulated classically and used to establish formulae half-integral weight modular forms Maaß forms.

In the classical Kostant–Souriau prequantization procedure, the Poisson algebra of a symplectic manifold (M,ω) is realized as the space of infinitesimal quantomorphisms of the prequantization circle bundle. Robinson and Rawnsley developed an alternative to the Kostant–Souriau quantization process in which the prequantization circle bundle and metaplectic structure for (M,ω) are replaced by a me...

We prove using a technique developed for GL n in Howe and Moy H a bijection between generalized Hecke algebras of G SL F over a p adic eld and those of its n fold metaplectic cover G This result implies that there is a canonical correspondence between irreducible admissible representations of G and genuine irreducible admissible representations of G of su ciently large level depending on n p

Abstract. We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin2r+1(C), which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel-King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman-Shalika for...

These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly SU(2). We give detailed examples, develop the techniques of twisted cohomology and gauge theory. We review Chern-Simons theory and describe an integrable system for the representation space of a surface. Final...