Let Y be a smooth projective irreducible curve defined over a finite field F q. We assume that G is a finite subgroup of the automorphism group of Y whose order divides q − 1. We show that relations among idempotents corresponding to the irreducible characters of subgroups H of G imply similar relations among generalized pranks of Y. We also relate this result to the realization of finite group...

Let G0 be a connected unipotent group over a finite field Fq, and let G = G0 ⊗Fq Fq, equipped with the Frobenius endomorphism Frq : G −→ G. For every character sheaf M on G such that Frq M ∼= M , we prove that M comes from an irreducible perverse sheaf M0 on G0 such that M0 is pure of weight 0 (as an `-adic complex) and for each integer n ≥ 1 the “trace of Frobenius” function tM0⊗FqFqn on G0(Fq...

We have seen that irreducible representations of a compact Lie group G can be constructed starting from a highest weight space and applying negative roots to a highest weight vector. One crucial thing that this construction does not easily tell us is what the character of this irreducible representation will be. The character would tell us not just which weights occur in the representation, but...

Title ofprogram: char Method ofsolution Murnaghan’s rule for the calculation of the irreducible charCatalogue number: AAMK acters of the symmetric group is implemented in a compact program. Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this issue) Restrictions on the complexity of the problem Limited only by available user memor...

The 2-modular decomposition numbers of the faithful irreducible ordinary characters of 3.McL are determined. The results are obtained by using the computer algebra packages Moc and Meat-Axe, and by applying condensation methods.

Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diag S(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand ...

Studied is an assumption on a group that ensures that no matter how the group is embedded in a symmetric group, the corresponding symmetrized tensor space has an orthogonal basis of standard (decomposable) symmetrized tensors.

Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if G is an M -group with odd order, then every irreducible character is super monomial. We prove that the conjecture is true if G is an M -group of odd order where every irreducible character is a {p}-lift for some prime p. We say that a group where irreducible cha...

Abstract It is known that irreducible cuspidal characters satisfy the preservation principle in Howe correspondences of finite reductive dual pairs. In this article, we generalize to any classical groups.

In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group G4. In particular, we classify the irreducible finite dimensional representations and compute their characters.