Categorification of (induced) cell modules and the rough structure of generalised Verma modules

• Autores: Volodymyr Mazorchuk, Catharina Stroppel
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 4, 2008, págs. 1363-1426
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.06.019
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• Resumen

  • This paper presents categorifications of (right) cell modules and induced cell modules for Hecke algebras of finite Weyl groups. In type A we show that these categorifications depend only on the isomorphism class of the cell module, not on the cell itself. Our main application is multiplicity formulas for parabolically induced modules over a reductive Lie algebra of type A, which finally determines the so-called rough structure of generalised Verma modules. On the way we present several categorification results and give a positive answer to Kostant's problem from [A. Joseph, Kostant's problem, Goldie rank and the Gelfand�Kirillov conjecture, Invent. Math. 56 (3) (1980) 191�213] in many cases. We also present a general setup of decategorification, precategorification and categorification.