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

TL;DR

This paper constructs and characterizes commutative subalgebras within the big shuffle algebra of cyclic type, generalizing previous work and connecting them to Bethe subalgebras of quantum affine gl(n).

Contribution

It introduces a new construction of commutative subalgebras in the big shuffle algebra and relates them to Bethe subalgebras of quantum affine gl(n).

Findings

Constructed commutative subalgebras of the big shuffle algebra.

Established a Bethe algebra realization of these subalgebras.

Connected the subalgebras to quantum affine gl(n) Bethe subalgebras.

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).