Robinson-Schensted Correspondence and Left Cells

Ariki, Susumu

doi:10.2969/aspm/02810001

Cited by 40 publications

(140 citation statements)

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“…The statements in (a) and (b) are due to Kazhdan-Lusztig [10, §5], but the proof given there is quite sketchy. A complete, self-contained proof, based on the methods in [10, §4], is given by Ariki [1]. The proof that we give here is different as far as the (more difficult) implications "⇒" are concerned.…”

Section: Applications To the Kazhdan-lusztig Cells In S Nmentioning

confidence: 99%

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Kazhdan–lusztig Cells and the Murphy Basis

Geck

2006

Proc. Lond. Math. Soc.

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Abstract. Let H be the Iwahori-Hecke algebra associated with Sn, the symmetric group on n symbols. This algebra has two important bases: the Kazhdan-Lusztig basis and the Murphy basis. While the former admits a deep geometric interpretation, the latter leads to a purely combinatorial construction of the representations of H, including the Dipper-James theory of Specht modules. In this paper, we establish a precise connection between the two bases, allowing us to give, for the first time, purely algebraic proofs for a number of fundamental properties of the Kazhdan-Lusztig basis and Lusztig's results on the a-function.

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Section: Applications To the Kazhdan-lusztig Cells In S Nmentioning

confidence: 99%

“…The proof that we give here is different as far as the (more difficult) implications "⇒" are concerned. Note also that (c) is neither proved in [10] nor in [1].…”

Section: Applications To the Kazhdan-lusztig Cells In S Nmentioning

confidence: 99%

Kazhdan–lusztig Cells and the Murphy Basis

Geck

2006

Proc. Lond. Math. Soc.

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“…As an application, we show that all of the conjectures in [20,Chap. 14] hold in this case, except possibly (P9), (P10) and (P15) 1 . We also determine the structure of the associated ring J.…”

Section: §1 Introductionmentioning

confidence: 99%

“…Let be the usual lexicographic order so that (i, j) < (i , j ) if i < i or if i = i and j < j . Then A 0 = Z[Γ 0 ] is nothing but the ring of Laurent polynomials in two independent indeterminates V 0 = e (1,0) and v 0 = e (0,1) . This is the set-up originally considered by Bonnafé-Iancu [2]; we may refer to this case as the "generic asymptotic case" in type B n .…”

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confidence: 99%

Lusztig’sa-Function in TypeB_nin the Asymptotic Case

Geck

Iancu

2006

Nagoya Mathematical Journal

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Abstract. In this paper, we study Lusztig's a-function for a Coxeter group with unequal parameters. We determine that function explicitly in the "asymptotic case" in type Bn, where the left cells have been determined in terms of a generalized Robinson-Schensted correspondence by Bonnafé and the second author. As a consequence, we can show that all of Lusztig's conjectural properties (P1)-(P15) hold in this case, except possibly (P9), (P10) and (P15). Our methods rely on the "leading matrix coefficients" introduced by the first author. We also interprete the ideal structure defined by the two-sided cells in the associated Iwahori-Hecke algebra Hn in terms of the Dipper-James-Murphy basis of Hn.

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“…This is especially relevant in light of the tableaux classification of Kazhdan-Lusztig cells. In type A, left Kazhdan-Lusztig cells consist of those permutations whose recording tableaux agree, see A. Joseph [5] or S. Ariki [2]. A similar result holds for the socalled asymptotic left cells in the Iwahori-Hecke algebras in type B, this time in terms of 2-multitableaux [3].…”

Section: Introductionmentioning

confidence: 62%