Bethe subalgebras of Uq(gln) via shuffle algebras

Boris Feigin; Alexander Tsymbaliuk

doi:10.1007/s00029-015-0212-z

Bethe subalgebras of U_q(gl_n) via shuffle algebras

Boris Feigin
, Alexander Tsymbaliuk

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we construct certain commutative subalgebras of the big shuffle algebra of type (Formula presented.). This can be considered as a generalization of the similar construction for the small shuffle algebra, obtained in Feigin et al. (J Math Phys 50(9):42, 2009). We present a Bethe algebra realization of these subalgebras. The latter identifies them with the Bethe subalgebras of (Formula presented.).

Original language	English
Pages (from-to)	979-1011
Number of pages	33
Journal	Selecta Mathematica, New Series
Volume	22
Issue number	2
DOIs	https://doi.org/10.1007/s00029-015-0212-z
State	Published - 1 Apr 2016
Externally published	Yes

Keywords

Bethe algebra
Drinfeld double
Shuffle algebra
Toroidal algebra

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

Access to Document

10.1007/s00029-015-0212-z

Cite this

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abstract = "In this article, we construct certain commutative subalgebras of the big shuffle algebra of type (Formula presented.). This can be considered as a generalization of the similar construction for the small shuffle algebra, obtained in Feigin et al. (J Math Phys 50(9):42, 2009). We present a Bethe algebra realization of these subalgebras. The latter identifies them with the Bethe subalgebras of (Formula presented.).",

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KW - Toroidal algebra

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