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arXiv · 1706.08747

Braid group action and root vectors for the $q$-Onsager algebra

Pascal Baseilhac·Stefan Kolb
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Abstract

We define two algebra automorphisms $T_0$ and $T_1$ of the $q$-Onsager algebra $B_c$, which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis for $B_c$. We show that the root vectors satisfy $q$-analogs of Onsager's original commutation relations. The paper is much inspired by I. Damiani's construction and investigation of root vectors for the quantized enveloping algebra of $\widehat{\mathfrak{sl}}_2$.

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Pascal Baseilhac, Stefan Kolb. 2017-06-27. Braid group action and root vectors for the $q$-Onsager algebra. https://arxiv.org/abs/1706.08747

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