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On a Certain Subalgebra of $U_q(\widehat{\mathfrak{sl}}_2)$ Related to the Degenerate $q$-Onsager Algebra
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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In [Kyushu J. Math. 64 (2010), 81–144], 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 $U'_q(\widehat{\mathfrak{sl}}_2)$, is generated by $e_0^+$, $e_1^\pm$, $k_i^{\pm1}$ $(i=0,1)$ with $e^-_0$ missing from the Chevalley generators $e_i^\pm$, $k_i^{\pm1}$ $(i=0,1)$ of $U_q(\widehat{\mathfrak{sl}}_2)$. In this paper, we determine the finite-dimensional irreducible representations of $U'_q(\widehat{\mathfrak{sl}}_2)$. Intertwiners are also determined.
Keywords: degenerate $q$-Onsager algebra; quantum affine algebra; TD-algebra; augmented TD-algebra; TD-pair. 
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     author = {Tomoya Hattai and Tatsuro Ito},
     title = {On {a~Certain} {Subalgebra} of $U_q(\widehat{\mathfrak{sl}}_2)$ {Related} to the {Degenerate} $q${-Onsager} {Algebra}},
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}
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Tomoya Hattai; Tatsuro Ito. On a Certain Subalgebra of $U_q(\widehat{\mathfrak{sl}}_2)$ Related to the Degenerate $q$-Onsager Algebra. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a6/

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