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

By Volodymyr Mazorchuk, C. Stroppel. 2007

101 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef95109cf0419a1c8bf6d9ab35a00c03518593cd

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Character D-modules via Drinfeld center of Harish-Chandra bimodules (2009, background): “It is interesting to compare it with the results of Mazorchuk and Stroppel [26], [27] which imply that for groups of type An the (right) cell subquotients in the abelian category of perverse sheaves are equivalent to the category of modules over a symmetric (in an alternative terminology, Frobenius)”
Endomorphisms of cell 2-representations (2012, unknown): “In [MS2], equivalence of cell 2 -representations corresponding to the same two-sided cell was obtained using Arkhipov’s twisting functors and the fact that they naturally commute with projective functors, see [AS].”
Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012, methodology): “Here, we give a categorical analogue of the decomposition (10) based on Gelfand–Kirillov dimension (which is directly connected with Lusztig’s a-function; see [46], Remark 42).”