Geodesic
A preorder-free construction of the Kazhdan-Lusztig representations of Hecke algebras $H_n(q)$ of symmetric groups
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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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. 
@article{DMTCS_2010_special_259_a69,
     author = {Buehrle, Charles and Skandera, Mark},
     title = {A preorder-free construction of the {Kazhdan-Lusztig} representations of {Hecke} algebras $H_n(q)$ of symmetric groups},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2874},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2874/}
}
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Buehrle, Charles; Skandera, Mark. A preorder-free construction of the Kazhdan-Lusztig representations of Hecke algebras $H_n(q)$ of symmetric groups. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2874. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2874/

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