Residue Formulae for the Trace on Affine Hecke Algebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915559273136128 |
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| author | Mammen, Paul |
| author_facet | Mammen, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Residue Formulae for the Trace on Affine Hecke Algebras Mammen, Paul Combinatorics Representation Theory 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. |
| title | Residue Formulae for the Trace on Affine Hecke Algebras |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2510.15169 |