Geodesic
Yang-Baxter basis of Hecke algebra and Casselman's problem (extended abstract)
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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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. 
@article{DMTCS_2020_special_379_a52,
     author = {Nakasuji, Maki and Naruse, Hiroshi},
     title = {Yang-Baxter basis of {Hecke} algebra and {Casselman's} problem (extended abstract)},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6370},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6370/}
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Nakasuji, Maki; Naruse, Hiroshi. Yang-Baxter basis of Hecke algebra and Casselman's problem (extended abstract). Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6370. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6370/

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