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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The fine structure of translation functors
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by Karen Günzl
Represent. Theory 3 (1999), 223-249
Published electronically: August 16, 1999


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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Bibliographic Information
  • Karen Günzl
  • Affiliation: Universität Freiburg Mathematisches Institut Eckerstr.1 D-79104 Freiburg Germany
  • Email:
  • 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:
  • MathSciNet review: 1714626