Specht modules and Kazhdan-Lusztig cells in type Bn

• Autores: Meinolf Geck, Lacrimioara Iancu, Christos Pallikaros
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 6, 2008, págs. 1310-1320
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.10.005
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• Resumen

  • Dipper, James and Murphy generalized the classical Specht module theory to the Hecke algebras of type Bn. On the other hand, for any choice of a monomial order on the parameters of type Bn, we obtain the corresponding Kazhdan�Lusztig cell modules. In this paper, we show that the Specht modules are naturally isomorphic to the Kazhdan�Lusztig cell modules if we choose the dominance order on the parameters, as in the �asymptotic case� studied by Bonnafé and the second named author. We also give examples which show that such an isomorphism does not exist for other choices of monomial orders.