Paradan's wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

TL;DR

This paper provides an elementary algebraic proof of Paradan's wall crossing formulae for partition functions, expressing the jumps via residue formulas and relating them through a generalized Khovanskii-Pukhlikov differential operator.

Contribution

It offers a new algebraic proof of wall crossing formulas and connects volume and partition function jumps using residue and differential operator techniques.

Findings

Elementary algebraic proof of wall crossing formulae

Expression of jumps via residue formulas

Relation between volume and partition functions established

Abstract

We give an elementary algebraic proof of Paradan's wall crossing formulae for partition functions. We also express such jumps in volume and partition functions by one dimensional residue formulae. Subsequently we reprove the relation between them as given by the application of a generalized Khovanskii-Pukhlikov differential operator.