Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$

HUANG Qian

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Jan. 2013

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HUANG Qian. Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 91-103, 114.

Citation:

HUANG Qian. Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 91-103, 114.

HUANG Qian. Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 91-103, 114.

Citation:

HUANG Qian. Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 91-103, 114.

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Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$

HUANG Qian

1.
Department of Mathematics, East China Normal University,Shanghai 200241, China

Received Date: 2012-02-01
Rev Recd Date: 2012-05-01
Publish Date: 2013-01-25

Abstract

Abstract

The fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under a certain group automorphism $\alpha$ with $\alpha\,(\widetilde{S}) = \widetilde{S}$ can be considered as the affine Weyl group ($\widetilde{C}_n,S$). Then the left and two-sided cells of the weighted Coxeter group ($\widetilde{C}_n,\widetilde{\ell}$), where $\widetilde{\ell}$ is the length function of $\widetilde{A}_{2n}$, can be given an explicit description by studying the fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under $\alpha$. We describe the cells of ($\widetilde{C}_n,\widetilde{\ell}$) corresponding to the partitions $\textbf{k}\textbf{1}^{\textbf{2n+1-k}}$ with $1\leqslant k \leqslant 2n+1$ and $(2n-1,2)$.
- affine Weyl groups,
- left cells,
- quasi-split case,
- weighted Coxeter group

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References(1)

References

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