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

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Abstract : We define two algebra automorphisms $T_0$ and $T_1$ of the q-Onsager algebra Bc, 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 Bc. 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 $\widehat{sl_2}$.
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Submitted on : Wednesday, November 18, 2020 - 8:30:30 PM
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Pascal Baseilhac, Stefan Kolb. Braid group action and root vectors for the q-Onsager algebra. Transformation Groups, Springer Verlag, 2020, 25 (June), pp.363-389. ⟨10.1007/s00031-020-09555-7⟩. ⟨hal-01549066⟩

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