The Fine Structure of Translation Functors
Representation Theory
2007-05-23 v1
Abstract
Let E be a simple finite dimensional representation of a semisimple Lie algebra with extremal weight nu and choose nonzero e in E_{nu}. Let M(tau) be the Verma module with highest weight tau and v_{tau} in M(tau)_{tau} its canonical generator. We investigate the projection of e \otimes v_{tau} in E \otimes M(tau) on the central character chi(tau + nu). This is a rational function in tau and we calculate its poles and zeros. We then apply this result in order to compare translation functors.
Keywords
Cite
@article{arxiv.math/9808117,
title = {The Fine Structure of Translation Functors},
author = {Karen Guenzl},
journal= {arXiv preprint arXiv:math/9808117},
year = {2007}
}
Comments
28 pages, LaTeX