Abstract
We define two algebra automorphisms Ͳ0 and Ͳ1 of the q-Onsager algebra \( {\mathcal{B}}_c \), 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 \( {\mathcal{B}}_c \). 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 \( \hat{\mathfrak{s}{\mathfrak{l}}_2} \).
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Pascal Baseilhac is Supported by C.N.R.S.
Stefan Kolb is Supported by EPSRC grant EP/K025384/1.
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BASEILHAC, P., KOLB, S. BRAID GROUP ACTION AND ROOT VECTORS FOR THE q-ONSAGER ALGEBRA. Transformation Groups 25, 363–389 (2020). https://doi.org/10.1007/s00031-020-09555-7
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DOI: https://doi.org/10.1007/s00031-020-09555-7