Left cells in type $B_n$ with unequal parameters

Details Left cells in type $B_n$ with unequal parameters Left cells in type $B_n$ with unequal parameters

2003-02-04

arxiv.org/abs/math/0302037v1

Mathematics

Representation Theory

26 pages

Scientific paper

Kazhdan and Lusztig have shown that the partition of the symmetric group of degree $n$ 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 for type $B_n$. We also give an explicit description of the left cell representations and show that they are irreducible and constructible.

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