If/ is an irreducible character of Sn, these functions are known as immanants; if/ is an irreducible character of some subgroup G of Sn (extended trivially to all of Sn by defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of Sn, respectively. We should po...

Let G be a finite group and Irr ( ) the set of all complex irreducible characters . The character-graph Δ associated to , is graph whose vertex primes which divide degrees some in two distinct p q are adjacent if product pq divides χ 1 for ∈ Tong-Viet posed conjecture that k -regular integer ⩾ 2 then either complete or cocktail party graph. In this paper, we show his true regular character-grap...

Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. We assume neither that the gr...

In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal sheaves. Irreducible representations of Hecke algebras associated to complex reflection groups at roots unity enter description. We do so by analysing Fourier transform nearby cycle constructed in [8].

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...

Abstract For an irreducible orthogonal character $$\chi $$ χ of even degree, there is a unique square class $$\det ({\chi })$$ det ( ) in the field such that invariant quadratic forms any L -representation affording have determinant })(...