Author:
BASEILHAC PASCAL,KOLB STEFAN
Abstract
AbstractWe define two algebra automorphisms Ͳ0 and Ͳ1 of the q-Onsager algebra $$ {\mathcal{B}}_c $$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 $$ {\mathcal{B}}_c $$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 $$ \hat{\mathfrak{s}{\mathfrak{l}}_2} $$sl2̂.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Reference21 articles.
1. J. Apel, U. Klaus, FELIX, http://felix.hgb-leipzig.de.
2. P. Baseilhac, Deformed Dolan–Grady relations in quantum integrable models, Nuclear Phys. B 709 (2005), no. 3, 491–521.
3. P. Baseilhac, S. Belliard, An attractive basis for the q-Onsager algebra, arXiv:[4]02950 (2017).
4. P. Baseilhac, S. Belliard, Generalized q-Onsager algebras and boundary affine Toda field theories, Lett. Math. Phys. 93 (2010) 213–228.
5. P. Baseilhac, S. Belliard, The half-infinite XXZ chain in Onsager's approach, Nucl. Phys. B 873 (2013), 550–583.
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