Quantum R-matrix and Intertwiners for the Kashiwara Algebra

Abstract

We study the algebra $B_q(\ge )$ presented by Kashiwara and introduce intertwiners similar to $q$-vertex operators. We show that a matrix determined by 2-point functions of the intertwiners coincides with a quantum R-matrix (up to a diagonal matrix) and give the commutation relations of the intertwiners. We also introduce an analogue of the universal R-matrix for the Kashiwara algebra.

21 pages

References in corpus (2)

• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Quantum affine symmetry in vertex models

Cited by in corpus (2)

• Crystal base of the negative half of the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$
• Fusion procedure for Yokonuma-Hecke algebras