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Representation Theory

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The fine structure of translation functors

Author: Karen Günzl
Journal: Represent. Theory 3 (1999), 223-249
MSC (1991): Primary 17B10
Published electronically: August 16, 1999
MathSciNet review: 1714626
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Abstract: Let $E$ be a simple finite-dimensional representation of a semisimple Lie algebra with extremal weight $\nu$ and let $0 \neq e \in E_{\nu}$. Let $M(\tau)$ be the Verma module with highest weight $\tau$ and $0 \neq v_{\tau} \in M(\tau)_{\tau}$. 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.

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Additional Information

Karen Günzl
Affiliation: Universität Freiburg Mathematisches Institut Eckerstr.1 D-79104 Freiburg Germany

Received by editor(s): September 2, 1998
Received by editor(s) in revised form: July 19, 1999
Published electronically: August 16, 1999
Additional Notes: Partially supported by EEC TMR-Network ERB FMRX-CT97-0100
Article copyright: © Copyright 1999 American Mathematical Society

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