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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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Affine geometric crystals in unipotent loop groups
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by Thomas Lam and Pavlo Pylyavskyy PDF
Represent. Theory 15 (2011), 719-728 Request permission

Abstract:

We study products of the affine geometric crystal of type $A$ corresponding to symmetric powers of the standard representation. The quotient of this product by the $R$-matrix action is constructed inside the unipotent loop group. This quotient crystal has a semi-infinite limit, where the crystal structure is described in terms of limit ratios previously appearing in the study of total positivity of loop groups.
References
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Additional Information
  • Thomas Lam
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 679285
  • ORCID: 0000-0003-2346-7685
  • Email: tfylam@umich.edu
  • Pavlo Pylyavskyy
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Address at time of publication: Department of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, Minnesota 55455
  • Email: ppylyavs@umn.edu
  • Received by editor(s): September 6, 2010
  • Received by editor(s) in revised form: June 29, 2011
  • Published electronically: December 1, 2011
  • Additional Notes: The first author was supported by NSF grant DMS-0652641 and DMS-0901111, and by a Sloan Fellowship.
    The second author was supported by NSF grant DMS-0757165.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 719-728
  • MSC (2010): Primary 17B37, 17B67, 22E65
  • DOI: https://doi.org/10.1090/S1088-4165-2011-00410-6
  • MathSciNet review: 2869015