Partial Gauss decomposition, \bf $U_q(\widehat{\mathfrak{gl}(n-1)})\in U_q(\widehat{\mathfrak{gl}(n)})$ and Zamolodchikov algebra

Abstract

We use the idea of partial Gauss decomposition to study structures related to $U_q(\widehat{\mathfrak{gl}(n-1)})$ inside $U_q(\widehat{\mathfrak{gl}(n)})$. This gives a description of $U_q(\widehat{\mathfrak{gl}(n)})$ as an extension of $U_q(\widehat{\mathfrak{gl}(n-1)})$ with Zamolodchikov algebras, We explain the connection of this new realization with form factors.

Amslatex, 8 pages