Regular representation on the big cell and big projective modules in the category O
Representation Theory
2007-05-23 v1 Quantum Algebra
Abstract
We study the algebra of regular functions on the big cell of the Gauss decomposition of a simple complex Lie group G. We prove that it is spanned by the matrix elements of big projective modules in the BGG category O, and admits a decomposition of Peter-Weyl type. The subspace of Whittaker vectors in the regular representation on the big cell gives a realization of the big projective modules in O, similar to the Borel-Weil theorem. These results can be extended to the quantum groups.
Cite
@article{arxiv.math/0410588,
title = {Regular representation on the big cell and big projective modules in the category O},
author = {Konstantin Styrkas},
journal= {arXiv preprint arXiv:math/0410588},
year = {2007}
}
Comments
24 pages