Representations of quantum affine algebras of type $B_N$
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- by Matheus Brito and Evgeny Mukhin PDF
- Trans. Amer. Math. Soc. 369 (2017), 2775-2806 Request permission
Abstract:
We study finite-dimensional representations of quantum affine algebras of type $B_N$. We show that a module is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized eigenspaces have dimension one. We classify all such modules and describe their $q$-characters. In some cases, the $q$-characters are described by super standard Young tableaux of type $(2N|1)$.References
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Additional Information
- Matheus Brito
- Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, Campinas - SP, Brazil, 13083-859
- Email: mbrito@ufpr.br
- Evgeny Mukhin
- Affiliation: Indiana University–Purdue University Indianapolis, 402 N. Blackford St, LD 270, Indianapolis, Indiana 46202
- MR Author ID: 317134
- Email: mukhin@math.iupui.edu
- Received by editor(s): November 18, 2014
- Received by editor(s) in revised form: April 14, 2015, and April 23, 2015
- Published electronically: August 18, 2016
- Additional Notes: The first author was supported by FAPESP, grants 2010/19458-9 and 2012/04656-5
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2775-2806
- MSC (2010): Primary 17B37; Secondary 81R50
- DOI: https://doi.org/10.1090/tran/6735
- MathSciNet review: 3592528