The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys–Murphy element involves many conjugacy classes with complicated coefficients. In this article we consider a combinatorial setup which allows us to manipulate such products easily: to...

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...

Let G be a quasi-split connected reductive group over a local eld of characteristic 0, and x a regular nilpotent element in the Lie algebra g of G. A theorem of Kostant then provides a canonical conjugacy class within each stable conjugacy class of regular semisimple elements in g. Normalized transfer factors take the value 1 on these canonical conjugacy classes. 1. Introduction Let k 0 be a lo...

As preparation for a duality theory for saddle programs, a partial conjugacy correspondence is developed among equivalence classes of saddle functions. Three known conjugacy correspondences, including Fenchel's correspondence among convex functions and Rockafellar's extension of it to equivalence classes of saddle functions, are shown to be degenerate special cases. Additionally, two new corres...

We describe a significantly improved algorithm for computing the conjugacy classes of a finite permutation group with trivial soluble radical. We rely on existing methods for groups that are almost simple, and we are concerned here only with the reduction of the general case to the almost simple case. Dedicated to Charles Leedham-Green on the occasion of his 65th birthday

Let Γ be a co-compact Fuchsian group (with no elliptic elements) and let Σ denote the associated hyperbolic surface H/Γ. Then Γ is isomorphic to the fundamental group of Σ and each non-trivial conjugacy class in Γ contains a unique closed geodesic on Σ. If we write l[γ] for the length of the closed geodesic in the conjugacy class [γ] then it was proved in [6] (though it was already implicit in ...

Abstract We study noncommutative differential structures on permutation groups SN , defined by conjugacy classes. The 2-cycles class defines an exterior algebra ΛN which is a super analogue of the quadratic algebra EN for Schubert calculus on the cohomology of the flag variety. Noncommutative de Rahm cohomology and moduli of flat connections are computed for N < 6. We find that flat connections...

Conjugacy classes of primitive words in the free group of rank two can indexed by the rationals. A representative for each conjugacy class is given by a recursive enumeration scheme and the representative, usually called a Farey word, is denoted by Wp/q where p and q are relatively prime integers. Primitive pairs, that is, pairs of words that generate the free group, correspond to pairs of word...

We prove a version of Valiron’s conjugacy theorem for Schur class mappings of the unit ball of C . As an application we obtain a formula for the spectral radius of composition operators on the ball with Schur class symbols.