Adams operations on classical compact Lie groups

Integration formulas for Brownian motion on classical compact Lie groups

Combinatorial formulas for the moments of the Brownian motion on classical compact Lie groups are obtained. These expressions are deformations of formulas of B. Collins and P. Śniady for moments of the Haar measure and yield a proof of the First Fundamental Theorem of Invariant and of classical Schur-Weyl dualities based on stochastic calculus.

Isospectral Metrics and Potentials on Classical Compact Simple Lie Groups

Given a compact Riemannian manifold (M,g), the eigenvalues of the Laplace operator ∆ form a discrete sequence known as the spectrum of (M,g). (In the case the M has boundary, we stipulate either Dirichlet or Neumann boundary conditions.) We say that two Riemannian manifolds are isospectral if they have the same spectrum. For a fixed manifold M , an isospectral deformation of a metric g0 on M is...

Probability on Compact Lie Groups

p–STUBBORN SUBGROUPS OF CLASSICAL COMPACT LIE GROUPS

induces an equivalence of Fp-homology [JMO, §§1-2]. This decomposition of BG, and the category Rp(G), play a central role in [JMO] and [JMO2] as a tool for describing sets of homotopy classes of maps fromBG to BH for any (other) compact connected Lie group H. But in most cases, explicit descriptions of the Rp(G), or explicit lists of the p-stubborn subgroups of G, were not necessary to obtain t...

Averages over Classical Compact Lie Groups and Weyl Characters

Abstract. We compute EG( ∏ i tr(g i)), where G = Sp(2n) or SO(m) (m = 2n, 2n + 1) with Haar measure. This was first obtained by Diaconis and Shahshahani [9], but our proof is more selfcontained and gives a combinatorial description for the answer. We also consider how averages of general symmetric functions EGΦn are affected when we introduce a Weyl character χλ into the integrand. We show that...