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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 11 (2015), 007, 13 pages      arXiv:1205.2946      https://doi.org/10.3842/SIGMA.2015.007
Contribution to the Special Issue on New Directions in Lie Theory

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

Tomoya Hattai a and Tatsuro Ito b
a) Iida Highschool, 1-1, Nonoe, Suzu, Ishikawa 927-1213, Japan
b) School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Hefei 230601, China

Received September 30, 2014, in final form January 15, 2015; Published online January 19, 2015

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 Uq(^sl2), is generated by e+0, e±1, k±1i (i=0,1) with e0 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 Uq(^sl2). Intertwiners are also determined.

Key words: degenerate q-Onsager algebra; quantum affine algebra; TD-algebra; augmented TD-algebra; TD-pair.

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References

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