An analogue of the correspondence betweenGL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K ⊂ GL(k) is one of the following: maximal parabolic, maximal torus, GL(k − 1) embedded diagonally. The generalised Legendre transform construction of hyperkähler metrics is studied further, showing that many known hyperkähler metrics (including the ...

Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...

The program of Langlands is studied here on the basis of: • new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; • the representations of the reductive algebraic groups GL(n) constituting the n-dimensional representations of the associated global Weil-Deligne groups; • a toroidal compactification of the conjugacy classes ...

We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms φ and ψ such that certain remnant words from φ are longer than the images of generators under ψ. Our first result is a remnant inequality condition which implies that two words u and v are not doubly-twisted conjugate. Further we show that if ψ is given and φ, u, and v are chosen at...

The program of Langlands is studied here on the basis of: • new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; • the representations of the reductive algebraic groups GL(n) constituting the n-dimensional representations of the associated global Weil-Deligne groups; • a toroidal compactification of the conjugacy classes ...

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...