Affine geometric crystals in unipotent loop groups
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- by Thomas Lam and Pavlo Pylyavskyy
- Represent. Theory 15 (2011), 719-728
- DOI: https://doi.org/10.1090/S1088-4165-2011-00410-6
- Published electronically: December 1, 2011
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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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Bibliographic 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