A new approach to Kostant's problem
2010 (English)In: Algebra & number theory, ISSN 1937-0652, Vol. 4, no 3, 231-254 p.Article in journal (Refereed) Published
For every involution w of the symmetric group S-n we establish, in terms of a special canonical quotient of the dominant Verma module associated with w, an effective criterion to verify whether the universal enveloping algebra U(sl(n)) surjects onto the space of all ad-finite linear transformations of the simple highest weight module L(w). An easy sufficient condition derived from this criterion admits a straightforward computational check (using a computer, for example). All this is applied to get some old and many new results, which answer the classical question of Kostant in special cases; in particular we give a complete answer for simple highest weight modules in the regular block of sl(n), n <= 5.
Place, publisher, year, edition, pages
2010. Vol. 4, no 3, 231-254 p.
IdentifiersURN: urn:nbn:se:uu:diva-97777ISI: 000276359100001OAI: oai:DiVA.org:uu-97777DiVA: diva2:172844