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Representation Theory
Representation Theory
ISSN 1088-4165

 

Affine geometric crystals in unipotent loop groups


Authors: Thomas Lam and Pavlo Pylyavskyy
Journal: Represent. Theory 15 (2011), 719-728
MSC (2010): Primary 17B37, 17B67, 22E65
Published electronically: December 1, 2011
MathSciNet review: 2869015
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Thomas Lam
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
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

DOI: http://dx.doi.org/10.1090/S1088-4165-2011-00410-6
PII: S 1088-4165(2011)00410-6
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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.