Categorification of (induced) cell modules and the rough structure of generalised Verma modules
2008 (English)In: Advances in Mathematics, ISSN 0001-8708, Vol. 219, no 4, 1363-1426 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2008. Vol. 219, no 4, 1363-1426 p.
generalised Verma modules, arbitrary irreducible module over a semisimple Lie algebra, Kazhdan-Lusztig cells, categorification, Gelfand-Zetlin modules, Hecke algebra, Kostant's problem
IdentifiersURN: urn:nbn:se:uu:diva-105795DOI: 10.1016/j.aim.2008.06.019ISI: 000259652400007OAI: oai:DiVA.org:uu-105795DiVA: diva2:222497