Geometric realizations and duality for Dahmen-Micchelli modules and De Concini-Procesi-Vergne modules

Abstract

We give an algebraic description of several modules and algebras related to the vector partition function, and we prove that they can be realized as the equivariant K-theory of some manifolds that have a nice combinatorial description. We also propose a more natural and general notion of duality between these modules, which corresponds to a Poincaré duality-type correspondence for equivariant K-theory.

Final version, to appear on Discrete and Computational Geometry

References in corpus (2)

• Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S
• Vector partition function and generalized Dahmen-Micchelli spaces

Cited by in corpus (3)

• Splines, lattice points, and arithmetic matroids
• On models of the braid arrangement and their hidden symmetries
• The arithmetic Tutte polynomials of the classical root systems