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

Volodymyr Mazorchuk, Catharina Stroppel

• 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.