ELA, Volume 13, pp. 1-9, January 2005, abstract.

A Family of Tridiagonal Pairs Related to the 
Quantum Affine Algebra U_q(\hat{sl_2})

Hasan Alnajjar and Brian Curtin

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(\hat{sl_2})-module on their 
underlying vector space. This is done by presenting 
an explicit basis for the underlying vector space 
and describing the U_q(\hat{sl_2})-action on that 
basis.