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

Understand

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).