On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra

Abstract

In [Kyushu J. Math. 64 (2010), 81-144], it is discussed that a certain subalgebra of the quantum affine algebra Uq(sl₂) controls the second kind TD-algebra of type I (the degenerate q-Onsager algebra). The subalgebra, which we denote by U'q(sl₂), is generated by e+0, e±₁, k±¹ i (i=0,1) with e−0 missing from the Chevalley generators e±i, k±¹i (i=0,1) of Uq(sl₂). In this paper, we determine the finite-dimensional irreducible representations of U′q(sl₂). Intertwiners are also determined.