Specht modules and Kazhdan--Lusztig cells in type $B_n$

Details Specht modules and Kazhdan--Lusztig cells in type $B_n$ Specht modules and Kazhdan--Lusztig cells in type $B_n$

2007-04-16

arxiv.org/abs/0704.1846v2

Mathematics

Representation Theory

the revised version corrects some minor errors

Scientific paper

Dipper, James and Murphy generalized the classical Specht module theory to Hecke algebras of type $B_n$. On the other hand, for any choice of a monomial order on the parameters in type $B_n$, we obtain corresponding Kazhdan--Lusztig cell modules. In this paper, we show that the Specht modules are naturally equivalent to the Kazhdan--Lusztig cell modules {\em if} we choose the dominance order on the parameters, as in the ``asymptotic case'' studied by Bonnaf\'e and the second named author. We also give examples which show that such an equivalence does not hold for other choices of monomial orders.

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