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0 Introduction In this paper we describe, for any given nite family of sub-spaces of a vector space or for linear subspaces in aane or projective space, a smooth model, proper over the given space, in which the complement of these subspaces is unchanged but the family of subspaces is replaced by a divisor with normal crossings. This model can be described… (More)
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)