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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 Steinberg-Lusztig tensor product theorem, Casselman-Shalika, and LLT polynomials
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by Martina Lanini and Arun Ram
Represent. Theory 23 (2019), 188-204
Published electronically: April 2, 2019


In this paper we establish a Steinberg-Lusztig tensor product theorem for abstract Fock space. This is a generalization of the type A result of Leclerc-Thibon and a Grothendieck group version of the Steinberg-Lusztig tensor product theorem for representations of quantum groups at roots of unity. Although the statement can be phrased in terms of parabolic affine Kazhdan-Lusztig polynomials and thus has geometric content, our proof is combinatorial, using the theory of crystals (Littelmann paths). We derive the Casselman-Shalika formula as a consequence of the Steinberg-Lusztig tensor product theorem for abstract Fock space.
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Bibliographic Information
  • Martina Lanini
  • Affiliation: School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3FD United Kingdom
  • MR Author ID: 990628
  • Email:
  • Arun Ram
  • Affiliation: Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010 Australia
  • MR Author ID: 316170
  • Email:
  • Received by editor(s): April 15, 2018
  • Received by editor(s) in revised form: January 31, 2019
  • Published electronically: April 2, 2019
  • Additional Notes: This research was partially supported by grants DP1201001942 and DP130100674.
    The first author was partially supported by Australian Research Council grant DP150103525. The first author also acknowledges the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.

  • Dedicated: Dedicated to Friedrich Knop and Peter Littelmann on the occasion of their 60th birthdays
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 188-204
  • MSC (2010): Primary 17B37; Secondary 20C20
  • DOI:
  • MathSciNet review: 3933899