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...

Solomon’s descent algebra is used to define a family of signed measures MW,x for a finite Coxeter group W and x > 0. The measures corresponding to W of type An arise from the theory of card shuffling. Formulas for these measures are obtained and conjectured in special cases. The eigenvalues of the associated Markov chains are computed. By elementary algebraic group theory, choosing a random sem...

We show that the conjugacy problem in a wreath product A ≀B is uniformTC -Turing-reducible to the conjugacy problem in the factors A and B and the power problem in B. Moreover, if B is torsion free, the power problem for B can be replaced by the slightly weaker cyclic submonoid membership problem for B, which itself turns out to be uniform-TC-Turing-reducible to conjugacy problem in A ≀B if A i...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. Using the Brauer complex, it is proved that this measure agrees with a second measure on conjugacy classes of the Weyl group in...

Let G be a linear connected semisimple Lie group. We denote by U(g)K the algebra of left invariant differential operators on G that are also right invariant by K, and Z(U(g)K) denotes center of U(g)K . In this paper we give a sufficient condition for a differential operator P ∈ Z(U(g)K) to have a fundamental solution on G. This result extends the same one obtained previously for real rank one L...

Let EG be a holomorphic principal G–bundle over a compact connected Riemann surface, where G is a connected reductive affine algebraic group defined over C, such that EG admits a holomorphic connection. Take any β ∈ H(X, ad(EG)), where ad(EG) is the adjoint vector bundle for EG, such that the conjugacy class β(x) ∈ g/G, x ∈ X , is independent of x. We give a sufficient condition for the existen...

In this paper we find a unique normal form for the symplectic matrix representation of the conjugacy class of a prime order element of the mapping-class group. We find a set of generators for the fundamental group of a surface with a conformal automorphism of prime order which reflects the action the automorphism in an optimal way. This is called an adapted homotopy basis and there is a corresp...

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 give an extension to coincidence theory of some key ideas from Nielsen fixed point theory involving remnant properties of free group homomorphisms. In particular we extend Wagner’s theorem for computing Reidemeister classes for Wagner characteristic homomorphisms, which allows us to compute doubly twisted conjugacy classes in many cases. We also extend Kim’s method for homomorphisms with bou...