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Left cells in type \(B_n\) with unequal parameters. (English) Zbl 1070.20004

Summary: 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.

MSC:

20C08 Hecke algebras and their representations
05E10 Combinatorial aspects of representation theory
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20C15 Ordinary representations and characters

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