On a Certain Subalgebra of U q ( sl ˆ 2 ) Related to the Degenerate q -Onsager Algebra
Abstract
In [Kyushu J. Math. 64 (2010), 81-144, arXiv:0904.2889], it is discussed that a certain subalgebra of the quantum affine algebra
U
q
(
sl
ˆ
2
)
controls the second kind TD-algebra of type I (the degenerate
q
-Onsager algebra). The subalgebra, which we denote by
U
′
q
(
sl
ˆ
2
)
, is generated by
e
+
0
,
e
±
1
,
k
±1
i
(i=0,1)
with
e
−
0
missing from the Chevalley generators
e
±
i
,
k
±1
i
(i=0,1)
of
U
q
(
sl
ˆ
2
)
. In this paper, we determine the finite-dimensional irreducible representations of
U
′
q
(
sl
ˆ
2
)
. Intertwiners are also determined.