The Denominators of Normalized RR-matrices of Types A2n1(2)A_{2n-1}^{(2)}, A2n(2)A_{2n}^{(2)}, Bn(1)B_{n}^{(1)} and Dn+1(2)D_{n+1}^{(2)}

  • Se-jin Oh

    Korea Institute for Advanced Study (KIAS), Seoul, South Korea

Abstract

The denominators of normalized RR-matrices provide important information on finite dimensional integrable representations over quantum affine algebras, and finite dimensional graded representations over quiver Hecke algebras by the generalized quantum affine Schur-Weyl duality functors. We compute the denominators of all normalized RR-matrices between fundamental representations of types A2n1(2)A_{2n-1}^{(2)} (n3)(n \ge 3), A2n(2)A_{2n}^{(2)} (n2)(n \ge 2), Bn(1)B_{n}^{(1)} (n3)(n \ge 3) and Dn+1(2)D_{n+1}^{(2)} (n2)(n \ge 2). Thus we can conclude that the normalized RR-matrices of types A2n1(2)A_{2n-1}^{(2)}, A2n(2)A_{2n}^{(2)}, Bn(1)B_{n}^{(1)} and D3(2)D_{3}^{(2)} have only simple poles, and of type Dn+1(2)D_{n+1}^{(2)} (n3)(n \ge 3) have double poles under certain conditions.

Cite this article

Se-jin Oh, The Denominators of Normalized RR-matrices of Types A2n1(2)A_{2n-1}^{(2)}, A2n(2)A_{2n}^{(2)}, Bn(1)B_{n}^{(1)} and Dn+1(2)D_{n+1}^{(2)}. Publ. Res. Inst. Math. Sci. 51 (2015), no. 4, pp. 709–744

DOI 10.4171/PRIMS/170