The Denominators of Normalized $R$-matrices of Types $A_{2n-1}^{(2)}$, $A_{2n}^{(2)}$, $B_{n}^{(1)}$ and $D_{n+1}^{(2)}$

Abstract

Denominators of normalized $R$-matrices provide important information on finite dimensional representations over quantum affine algebras, and over quiver Hecke algebras by the generalized quantum affine Schur-Weyl duality functors. We compute the denominators of all normalized $R$-matrices between fundamental representations of types $A_{2n-1}^{(2)}$, $A_{2n}^{(2)}$, $B_{n}^{(1)}$ and $D_{n+1}^{(2)}$. Thus we can conclude that the normalized $R$-matrices of types $A_{2n-1}^{(2)}$, $A_{2n}^{(2)}$, $B_{n}^{(1)}$ have only simple poles, and of type $D_{n+1}^{(2)}$ have double poles under certain conditions.