Charles Buehrle ; Mark Skandera
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A preorder-free construction of the Kazhdan-Lusztig representations of Hecke algebras Hn(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)
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https://doi.org/10.46298/dmtcs.2874
A preorder-free construction of the Kazhdan-Lusztig representations of Hecke algebras Hn(q) of symmetric groups Conference paper
Authors: Charles Buehrle 1; Mark Skandera 1
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Charles Buehrle;Mark Skandera
1 Department of Mathematics
We use a quantum analog of the polynomial ring Z[x1,1,…,xn,n] to modify the Kazhdan-Lusztig construction of irreducible Hn(q)-modules. This modified construction produces exactly the same matrices as the original construction in [Invent. Math.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.