In this paper, we present formulas for the number of decompositions of elements of the Weyl groups of type A., D. and B, as products of a number of reflections that is not necessarily minimal. For this purpose, we consider the poset of conjugacy classes of W introduced in B6dard and Goupil (1992) for the symmetric group. This poset describes the action of the set of reflections of a reflection ...

In this paper, we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper. AMS 2000 Mathematics Subject Classification: Primary 60J45, 3...

Inspiration: Simple noncompact connected Lie groups — Irreducible symmetric spaces of noncompact type (E.Cartan et al). Here there is an essentially 1-1 correspondence between algebraic objects (a Lie group of a certain type) and geometric objects (certain symmetric spaces). Namely, given a Lie group G on constructs a symmetric space X = G/K (K is a maximal compact subgroup of G) and, conversel...

It is shown that central elements in G. Letzter’s quantum group analogs of symmetric pairs lead to solutions of the reflection equation. This clarifies the relation between Letzter’s approach to quantum symmetric pairs and the approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen. We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type construction of quantum symmetric pairs...

Reflection equation algebras and related Uq(g)-comodule algebras appear in various constructions of quantum homogeneous spaces and can be obtained via transmutation or equivalently via twisting by a cocycle. In this paper we investigate algebraic and representation theoretic properties of such so called ‘covariantized’ algebras, in particular concerning their centres, invariants, and characters...

Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with reflection-symmetric topologies, we derive a new lower bound for the one-constant elastic energy. For certain topologies, called conformal and anticonformal, th...