English

Yang-Baxter basis of Hecke algebra and Casselman's problem (extended abstract)

Representation Theory 2025-03-25 v3

Abstract

We generalize the definition of Yang-Baxter basis of type AA Hecke algebra introduced by A.Lascoux, B.Leclerc and J.Y.Thibon (Letters in Math. Phys., 40 (1997), 75--90) to all the Lie types and prove their duality. As an application we give a solution to Casselman's problem on Iwahori fixed vectors of principal series representation of pp-adic groups.

Keywords

Cite

@article{arxiv.1512.04485,
  title  = {Yang-Baxter basis of Hecke algebra and Casselman's problem (extended abstract)},
  author = {Maki Nakasuji and Hiroshi Naruse},
  journal= {arXiv preprint arXiv:1512.04485},
  year   = {2025}
}

Comments

12 pages.Ver.3 Proposition 7,8 are corrected. These formulae are not used by other parts of this paper