We show how, by making use of a new basis of the IIB supergravity axion-dilaton coset, SL(2,R)/SO(2), 7-branes that belong to different conjugacy classes of the duality group SL(2,R) naturally couple to IIB supergravity with appropriate source terms characterized by an SL(2,R) charge matrix Q. The conjugacy classes are determined by the value of the determinant of Q. The (p, q) 7-branes are the...

In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This resul...

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...

We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some ex...

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...

We solve the following problem: Let M be a 2g × 2g symplectic matrix of prime order with integer entries. Find a unique normal form for M , that is, a symplectic matrix whose entries are determined by its conjugacy invariants. This is equivalent to finding a unique normal form for the matrix representation of the conjugacy class of a prime order element of the mapping class group.

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...

Solution. Henceforth, for the sake of notation when we must use variables, let i denote the element i+ k in the symmetric group on n elements, where i+ k ≤ n. S1 is the trivial group, so has one conjugacy class. S2 is abelian, so it has two conjugacy classes of one element each. We proved in class that cycle type is invariant under conjugation, so every conjugacy class may contain only one cycl...

We analyze a class of deformations of Anosov diffeomorphisms: these C-small, but C-macroscopic deformations break the topological conjugacy class but leave the high entropy dynamics unchanged. More precisely, there is a partial conjugacy between the deformation and the original Anosov system that identifies all invariant probability measures with entropy close to the maximum. We also establish ...

Affine Deligne-Lusztig varieties are analogs of DeligneLusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine DeligneLusztig varieties (for a split group and a basic σ-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a...