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

Volodymyr Mazorchuk; Catharina Stroppel

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arXiv · math/0702811

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

Volodymyr Mazorchuk·Catharina Stroppel

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Abstract

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 generalized Verma modules. On the way we present several categorification results and give the positive answer to Kostant's problem from \cite{Jo} in many cases. We also give a general setup of decategorification, precategorification and categorification.

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BibTeX RIS

Volodymyr Mazorchuk, Catharina Stroppel. 2007-02-27. Categorification of (induced) cell modules and the rough structure of generalized Verma modules. https://arxiv.org/abs/math/0702811

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