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

Mazorchuk, V. and Stroppel, C. (2008) Categorification of (induced) cell modules and the rough structure of generalised Verma modules. Advances in Mathematics, 219(4), pp. 1363-1426. (doi: 10.1016/j.aim.2008.06.019)

Abstract

This paper presents categorifications of (right) cell modules and induced cell modules for Hecke algebras of finite Weyl groups. fit 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stroppel, Dr Catharina
• Authors: Mazorchuk, V., and Stroppel, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Mathematics
• ISSN: 0001-8708