Kostant Modules in Blocks of Category S

In this article, the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category S for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L "looks like" the cohomology with coefficients...

Full description

Saved in:
Bibliographic Details
Published inCommunications in algebra Vol. 37; no. 1; pp. 323 - 356
Main Authors Boe, Brian D., Hunziker, Markus
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 12.01.2009
Subjects
BGG resolution
Hermitian symmetric pair
Kostant module
Minimal free resolution
Parabolic category
Primary 17B10
Rationally smooth Schubert variety
Secondary 17B56, 14M15
Online AccessGet full text

Cover

More Information
Summary:In this article, the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category S for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L "looks like" the cohomology with coefficients in a finite-dimensional module, as in Kostant's theorem. A complete classification of these "Kostant modules" in regular blocks for maximal parabolics in the simply laced types is given. A complete classification is also given in arbitrary (singular) blocks for Hermitian symmetric categories.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870802243937