  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).
