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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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The fine structure of translation functors
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by Karen Günzl PDF
Represent. Theory 3 (1999), 223-249 Request permission

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
  • Email: karen@mathematik.uni-freiburg.de
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 223-249
  • MSC (1991): Primary 17B10
  • DOI: https://doi.org/10.1090/S1088-4165-99-00056-4
  • MathSciNet review: 1714626