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A new algorithm for
finding an l.c.r. set in certain two-sided cells
Jian-yi Shi |
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Vol. 256 (2012), No. 1, 235–252
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Abstract |
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Let (W,S) be an irreducible Weyl or affine Weyl group. In 1994, we constructed an algorithm for finding a representative set of left cells (or an l.c.r. set for short) of W in a two-sided cell Ω. Here, we introduce a new simpler algorithm for finding an l.c.r. set of W in Ω when the subset F(Ω) of Ω is known. We introduce some technical tricks by some examples for applying the algorithm and for finding the set F(Ω). The resulting set E(Ω) is useful in verifying a conjecture of Lusztig that any left cell in an affine Weyl group is left-connected. |
Keywords
affine Weyl groups, left cells, two-sided cells, alcove
forms, algorithm
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Mathematical Subject Classification 2010
Primary: 20F55
Secondary: 20C08
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Milestones
Received: 9 April 2011
Revised: 7 December 2011
Accepted: 31 December 2011
Published: 6 May 2012
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Authors |
| Jian-yi Shi | |
| Department of Mathematics East China Normal University 500 Dongchuan Road Shanghai 200241 China |
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