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

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).

v1: 21 pages; v2: 23 pages, minor corrections, some details added

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