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Categorification of (induced) cell modules and the rough structure of generalised Verma modules
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Algebra)
2008 (English)In: Advances in Mathematics, ISSN 0001-8708, Vol. 219, no 4, 1363-1426 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
generalised Verma modules, arbitrary irreducible module over a semisimple Lie algebra, Kazhdan-Lusztig cells, categorification, Gelfand-Zetlin modules, Hecke algebra, Kostant's problem
National Category
URN: urn:nbn:se:uu:diva-105795DOI: 10.1016/j.aim.2008.06.019ISI: 000259652400007OAI: oai:DiVA.org:uu-105795DiVA: diva2:222497
Available from: 2009-06-08 Created: 2009-06-08 Last updated: 2009-08-27Bibliographically approved

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Algebra, Geometry and Logic
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