In this lecture we start to study the representation theory of the symmetric groups Sn over C. Let us summarize a few things that we already know. 0) A representation of Sn is the same thing as a representation of the group algebra CSn. 1) As with all finite groups, any representation of Sn over C is completely reducible. 2) The number of irreducible representations of Sn coincides with the num...

Conjugacy separability of any group of the class of one-relator groups given by the presentation 〈a, b; [am, bn] = 1〉 (m, n > 1) is proven.

We study solutions of the Riemann boundary value problem in class Cauchy type integrals with densities from grand Lebesgue spaces domains nonsmooth boundaries. The case piecewise conjugacy coefficients is studied.

of distributions. The terms on the right are parametrized by "cuspidal automorphic data", and are defined in terms of Eisenstein series. They have been evaluated rather explicitly in [3]. The terms on the left are parametrized by semisimple conjugacy classes and are defined in terms of related G(A) orbits. The object of this paper is to evaluate these terms. In previous papers we have already e...

We study representations related to the conjugacy action of the symmetric group. These arise as sums of submodules induced from centraliser subgroups, and their Frobenius characteristics have elegant descriptions, often as a multiplicity-free sum of power-sum symmetric functions. We describe a general framework in which such representations, and consequently such linear combinations of power-su...

We study a class of perverse sheaves on the variety of pairs (P, gUP ) where P runs through a conjugacy class of parabolics in a connected reductive group and gUP runs through G/UP . This is a generalization of the theory of character sheaves. 2000 Math. Subj. Class. 20G99.