Induction and Restriction of Kazhdan–Lusztig Cells

✍ Scribed by Yuval Roichman

• Book ID: 102562474
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 252 KB
• Volume: 134
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1997.1712

✦ Synopsis

Barbasch and Vogan gave a beautiful rule for restricting and inducing Kazhdan Lusztig representations of Weyl groups. In this paper we show that this rule implies and generalizes the Littlewood Richardson rule for decomposing outer products of representations of the symmetric groups. A new recursive rule for computing characters of arbitrary Coxeter groups follows. Another application is a generalization of Garsia Remmel's algorithm for decomposing certain tensor products of symmetric groups representations.

1998 Academic Press 1.2. The Littlewood Richardson rule gives a combinatorial procedure to decompose the outer products of representations of the symmetric groups. Schu tzenberger [Sc] suggested a new version to the Littlewood Richardson rule, using the language of Knuth equivalence classes.

The Knuth equivalence classes are the Kazhdan Lusztig cells of the symmetric groups. This gives rise to the question whether it is possible to generalize Schu tzenberger's results to arbitrary Coxeter groups. A positive answer to this question is given in this paper.

1. 3

The Murnaghan Nakayama rule is an efficient recursive rule for computing characters of the symmetric groups (cf. [JK, 2.4]). Our goal is finding a general recursive rule for characters of arbitrary Coxeter groups.