It is proved that the centre Z of the simply connected quantised universal enveloping algebra over C, U ε,P (sl n), ε a primitive lth root of unity, l an odd integer > 1, has a rational field of fractions. Furthermore it is proved that if l is a power of an odd prime, Z is a unique factorisation domain.
Motivated by the counting formulas of integral polytopes as in Brion–Vergne ,  and Szenes–Vergne , we start to lie the foundations of a theory for toric arrangements, which may be considered as the periodic version of the theory of hyperplane arrangements.
O. INTRODUCTION 0.1. Let X be a linear transformation of a finite-dimensional vector space V. The configuration of flags in V which are fixed by X has rather remarkable properties when X is unipotent. Though this case is especially interesting, the proper generality in which to study such configurations is in the theory of reductive algebraic groups, where… (More)
This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory will appear in . Here we introduce a space of functions on a lattice which generalizes the space of… (More)
We study the quotient of a completion of a symmetric variety G/H under the action of H. We prove that this is isomorphic to the closure of the image of an isotropic torus under the action of the restricted Weyl group. In the case the completion is smooth and toroidal we describe the set of semistable points.
We use the results of ,  to discuss the counting formulas of network flow polytopes and magic squares, i.e. the formula for the corresponding Ehrhart polynomial in terms of residues. We also discuss a description of the big cells using the theory of non broken circuit bases.