English

Residue Formulae for the Trace on Affine Hecke Algebras

Combinatorics 2025-10-20 v1 Representation Theory

Abstract

Motivated by recent advances in Catalan combinatorics, we study special values of the standard trace on affine Hecke algebras. Starting from a generating function for this trace calculated by Opdam, we use the theory of Szenes and Vergne to obtain residue formulae for the trace. This allows us to derive a product formula for the trace of translation elements corresponding to weights in certain ``Big Chambers'' of the positive root cone.

Keywords

Cite

@article{arxiv.2510.15169,
  title  = {Residue Formulae for the Trace on Affine Hecke Algebras},
  author = {Paul Mammen},
  journal= {arXiv preprint arXiv:2510.15169},
  year   = {2025}
}