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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Twisted Yangians, twisted quantum loop algebras and affine Hecke algebras of type $ BC$


Authors: Hongjia Chen, Nicolas Guay and Xiaoguang Ma
Journal: Trans. Amer. Math. Soc. 366 (2014), 2517-2574
MSC (2010): Primary 17B37, 20C08
Published electronically: January 31, 2014
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Abstract: We study twisted Yangians of type AIII which have appeared in the literature under the name of reflection algebras. They admit $ q$-versions which are new twisted quantum loop algebras. We explain how these can be defined equivalently either via the reflection equation or as coideal subalgebras of Yangians of $ \mathfrak{gl}_n$ (resp. of quantum loop algebras of $ \mathfrak{gl}_n$). The connection with affine Hecke algebras of type $ BC$ comes from a functor of Schur-Weyl type between their module categories.


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Additional Information

Hongjia Chen
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: hjchenmath@gmail.com

Nicolas Guay
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
Email: nguay@ualberta.ca

Xiaoguang Ma
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China
Email: xgma@math.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05994-1
PII: S 0002-9947(2014)05994-1
Received by editor(s): January 1, 2012
Received by editor(s) in revised form: July 6, 2012
Published electronically: January 31, 2014
Additional Notes: The second author was supported by an NSERC Discovery Grant. Special thanks to Alexander Molev for answering some of our questions and to M. Nazarov for a copy of his unpublished note and for allowing us to reproduce the proof of one of his results, namely Theorem 4.7
The third author was supported by a Postdoctoral Fellowship of the Pacific Institute for the Mathematical Sciences.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.