Charles Buehrle ; Mark Skandera - A preorder-free construction of the Kazhdan-Lusztig representations of Hecke algebras $H_n(q)$ of symmetric groups

dmtcs:2874 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2874
A preorder-free construction of the Kazhdan-Lusztig representations of Hecke algebras $H_n(q)$ of symmetric groups Article

Authors: Charles Buehrle 1; Mark Skandera 1

  • 1 Department of Mathematics

We use a quantum analog of the polynomial ring $\mathbb{Z}[x_{1,1},\ldots, x_{n,n}]$ to modify the Kazhdan-Lusztig construction of irreducible $H_n(q)$-modules. This modified construction produces exactly the same matrices as the original construction in [$\textit{Invent. Math.}$ $\textbf{53}$ (1979)], but does not employ the Kazhdan-Lusztig preorders. Our main result is dependent on new vanishing results for immanants in the quantum polynomial ring.

https://doi.org/10.46298/dmtcs.2874
Source: HAL:hal-01186303v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Kazhdan-Lusztig,immanants,irreducible representations,Hecke algebra,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)

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