Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be total words (or simply words). Given an infinite partial word w, the number of distinct total words over the alphabet that are compatible with factors of w of a given length, called subwords of w, refers to...

It is shown that the full symmetry class of tensors associated with the irreducible character [2, 1n−2] of Sn does not have an orthogonal basis consisting of decomposable symmetrized tensors.

The character formula of any finite dimensional irreducible module Lλ for Lie superalgebra osp(n|2) is computed. As a by-product, the decomposition of tensor module Lλ ⊗ C n|2, where Cn|2 is the natural representation, is obtained.

The aim of this paper is to show that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class. MSC 2000: 20C15

The article gives explicit values of some constants which appear in the character formula for the irreducible supercuspidal representation of GLl(F ) for F a local field of the residual characteristic p = l.

For the quaternion division algebra D over a non-Archimedean local field k, and π an irreducible finite dimensional representation of D×, say with trivial central character, we prove the existence of a quadratic extension K of k such that the trivial character of K× appears in π, as well as the existence of a quadratic extension L of k such that the trivial character of L× does not appear in π....

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...

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 complex reductive algebraic group and let Γ be a finitely generated group. In this paper we study properties of irreducible and completely reducible representations ρ : Γ → G in the context of the geometric invariant theory of the G-action on Hom(Γ, G) by conjugation. In particular, we prove that ρ is poly-stable (i.e. its orbit is closed) if and only if ρ is completely reducible. We...

We account some detailed calculation of irreducible character values $G_n$ with application to estimate fiber size the commutator map over regular semisimple and central elements $\SL_n$.