Pseudo-Permutations II: Geometry and Representation Theory

Abstract

In this paper, we provide the second part of the study of the pseudo-permutations. We first derive a complete analysis of the pseudo-permutations, based on hyperplane arrangements, generalizing the usual way of translating the permutations. We then study the module of the pseudo-permutations over the symmetric group and provide the characteristics of this action.

Keywords

• hyperplane arrangements
• symmetric group
• permutations
• q-analogs
• [info] computer science [cs]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]