A family of tridiagonal pairs related to the quantum affine algebra U_q(sl_2)

Abstract

A type of tridiagonal pair is considered, said to be mild of q-Serre type. It is shown that these tridiagonal pairs induce the structure of a quantum affine algebra U_q(sl₂)-module on their underlying vector space.This is done by presenting an explicit basis for the underlying vector space and describing the U_q(sl₂)-action on that basis.