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Representation Theory

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Left cells in type $B_n$ with unequal parameters

Authors: Cédric Bonnafé and Lacrimioara Iancu
Journal: Represent. Theory 7 (2003), 587-609
MSC (2000): Primary 20C08; Secondary 20C15
Published electronically: November 19, 2003
MathSciNet review: 2017068
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Abstract: Kazhdan and Lusztig have shown that the partition of the symmetric group ${\mathfrak{S}}_n$ into left cells is given by the Robinson-Schensted correspondence. The aim of this paper is to provide a similar description of the left cells in type $B_n$ for a special class of choices of unequal parameters. This is based on a generalization of the Robinson-Schensted correspondence in type $B_n$. We provide an explicit description of the left cell representations and show that they are irreducible and constructible.

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Additional Information

Cédric Bonnafé
Affiliation: Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France

Lacrimioara Iancu
Affiliation: Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France — and — Facultatea de Stiinte, Universitatea de Nord Baia Mare, Victoriei 76, RO-4800 Baia Mare, Romania

Received by editor(s): February 4, 2003
Received by editor(s) in revised form: September 17, 2003
Published electronically: November 19, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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