On a Certain Subalgebra of $U_q({\widehat{\mathfrak{sl}}}_2)$ 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 $U_q({\widehat{\mathfrak{sl}}}_2)$ controls the second kind TD-algebra of type I (the degenerate $q$-Onsager algebra). The subalgebra, which we denote by $U_q^{\prime }({\widehat{\mathfrak{sl}}}_2)$, is generated by $e_0^{+}$, $e_1^{\pm }$, $k_i^{\pm 1}$ $(i=0,1)$ with $e_0^{-}$ missing from the Chevalley generators $e_i^{\pm }$, $k_i^{\pm 1}$ $(i=0,1)$ of $U_q({\widehat{\mathfrak{sl}}}_2)$. In this paper, we determine the finite-dimensional irreducible representations of $U_q^{\prime }({\widehat{\mathfrak{sl}}}_2)$. Intertwiners are also determined.

References in corpus (1)

• Some algebra related to $P$-and $Q$-polynomial association schemes

Cited by in corpus (1)

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