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

Maki Nakasuji (1) , Hiroshi Naruse (2)

1 Sophia University [Tokyo]
2 Yamanashi University

We generalize the definition of Yang-Baxter basis of type A 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 p-adic groups.

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

Maki Nakasuji, Hiroshi Naruse. Yang-Baxter basis of Hecke algebra and Casselman's problem (extended abstract). 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6370⟩. ⟨hal-02166345⟩