Kostant's problem and parabolic subgroups
2010 (English)In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 52, 19-32 p.Article in journal (Refereed) Published
Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I subset of S let g(I) be the corresponding semi-simple subalgebra of g. Denote by W-I the Weyl group of g(I) and let w(o) and w(o)(I) be the longest elements of W and W-I, respectively In this paper we show that the answer to Kostant's problem, i.e. whether the Universal enveloping algebra subjects onto the space of all ad-finite linear transformations of a given module, is the same for the simple highest weight g(I)-module L-I(x) of highest weight x . 0, x is an element of W-I, as the answer for the simple highest weight g-module L(xw(o)(l)w(o)) of highest weight xw(o)(I)w(o). 0. We also give a new description Of the unique quasi-simple quotient of the Verma module Delta(e) with the same annihilator as L(y), y is an element of W.
Place, publisher, year, edition, pages
2010. Vol. 52, 19-32 p.
IdentifiersURN: urn:nbn:se:uu:diva-97778DOI: 10.1017/S0017089509990127ISI: 000273383200002OAI: oai:DiVA.org:uu-97778DiVA: diva2:172845