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...

Throughout the paper,M will always denote a complete, orientable finite volume hyperbolic 3-manifold with cusps. By abuse of notation we will denote by ∂M to be the boundary of the compact manifold obtained from M by truncating the cusps. Given such a manifold, the SL2(C) character variety of M , X(M), is a complex algebraic set associated to representations of π1(M)→ SL2(C) (see §4 for more de...

Let G be a connected, simply-connected, almost simple algebraic group of simplylaced type over C and let σ be a diagram automorphism of G. Let Gσ = ((G)) be the L-dual of the fixed point subgroup of σ on the L-dual of G. In this paper we relate the character of a finite dimensional irreducible representation of the disconnected algebraic group G〈σ〉 (generated by G and σ) on the connected compon...

Making use of a Howe duality involving the infinite-dimensional Lie superalgebra ĝl∞|∞ and the finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of ĝl∞|∞ in terms of hook Schur functions. We use the reduction procedure of ĝl∞|∞ to ĝln|n to derive a character formula for a certain class of level 1 highest weight ir...

We consider the full multinomial combinatorics of all irreducible representations of the octahedral (cubic) symmetry as a function of partitions for vertex, face and edge colorings. Full combinatorial tables for all irreducible representations and all multinomial partitions are constructed. These enumerations constitute multinomial expansions of character-based cycle index polynomials, and grow...

Let g be a semisimple Lie algebra, and let h be a reductive subalgebra of maximal rank in g. Given any irreducible representation of g, consider its tensor product with the spin representation associated to the orthogonal complement of h in g. Recently, B. Gross, B. Kostant, P. Ramond, and S. Sternberg [2] proved a generalization of the Weyl character formula which decomposes the signed charact...