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arXiv · 1012.2195

Kazhdan-Lusztig basis for generic Specht modules

Yunchuan Yin
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Abstract

In this paper, we let $\Hecke$ be the Hecke algebra associated with a finite Coxeter group $W$ and with one-parameter, over the ring of scalars $\Alg=\mathbb{Z}(q, q^{-1})$. With an elementary method, we introduce a cellular basis of $\Hecke$ indexed by the sets $E_J (J\subseteq S)$ and obtain a general theory of "Specht modules". We provide an algorithm for $W\!$-graphs for the "generic Specht module", which associates with the Kazhdan and Lusztig cell ( or more generally, a union of cells of $W$ ) containing the longest element of a parabolic subgroup $W_J$ for appropriate $J\subseteq S$. As an example of applications, we show a construction of $W\!$-graphs for the Hecke algebra of type $A$.

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BibTeXRIS

Yunchuan Yin. 2010-12-10. Kazhdan-Lusztig basis for generic Specht modules. https://arxiv.org/abs/1012.2195

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