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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Representations of quantum affine algebras of type $ B_N$


Authors: Matheus Brito and Evgeny Mukhin
Journal: Trans. Amer. Math. Soc. 369 (2017), 2775-2806
MSC (2010): Primary 17B37; Secondary 81R50
DOI: https://doi.org/10.1090/tran/6735
Published electronically: August 18, 2016
MathSciNet review: 3592528
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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\vert 1)$.


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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
Email: mukhin@math.iupui.edu

DOI: https://doi.org/10.1090/tran/6735
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
Article copyright: © Copyright 2016 American Mathematical Society

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