We prove that the duality operator preserves the Frobenius–Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius–Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius–Schur indicators of certain real-valued, i...

For irreducible characters {χq |λ ` n}, induced sign characters { q |λ ` n}, and induced trivial characters {ηλ q |λ ` n} of the Hecke algebra Hn(q), and KazhdanLusztig basis elements C ′ w(q) with w avoiding the patterns 3412 and 4231, we combinatorially interpret the polynomials χq (q `(w)/2C ′ w(q)), λ q (q `(w)/2C ′ w(q)), and ηλ q (q `(w)/2C ′ w(q)). This provides a new algebraic interpret...

Let U and A be algebras over a field k. We study algebra structures H on the underlying tensor product U⊗A of vector spaces which satisfy (u⊗a)(u′⊗a′) = uu′⊗aa′ if a = 1 or u′ = 1. For a pair of characters ρ ∈ Alg(U, k) and χ ∈ Alg(A, k) we define a left H-module L(ρ, χ). Under reasonable hypotheses the correspondence (ρ, χ) 7→ L(ρ, χ) determines a bijection between character pairs and the isom...

where k (p) is the +1 (−1) eigenspace of θ on g. Let Z(g) be the center of the universal enveloping algebra of g, and fix a character χ of Z(g). Let HC be the category of Harish-Chandra modules for G (i.e. finitely generated (g,K)–modules), and let HCχ be the full subcategory of HC of the modules with generalized central character χ. We are interested in the distribution characters, say, of the...