Bethe subalgebras of quantum affine gl(n) via shuffle algebras

Authors :: Feigin, Boris
Tsymbaliuk, Alexander
Source :: Selecta Math. New Series 22 (2016), no. 2, 979-1011
Publication Year :: 2015
Abstract: In this article, we construct certain commutative subalgebras of the big shuffle algebra of cyclic type. This can be considered as a generalization of the similar construction for the small shuffle algebra, obtained by Feigin-Hashizume-Hoshino-Shiraishi-Yanagida. We present a Bethe algebra realization of these subalgebras. The latter identifies them with the Bethe subalgebras of quantum affine gl(n).<br />Comment: v1: 21 pages; v2: 23 pages, minor corrections, some details added