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A new PBW basis for the alternating central extension of the q-Onsager algebra
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DOI：10.1016/j.nuclphysb.2026.117577.png)
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Abstract
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We establish a new PBW basis for Aq, the alternating central extension of the q-Onsager algebra. Terwilliger showed that the alternating generators form a PBW basis in the block order G<W−<W+<G˜. We prove that they also form a PBW basis in the different block order W−<G<G˜<W+. Consequently, multiplication induces a vector-space isomorphism W−⊗G⊗G˜⊗W+⟶Aq,thereby confirming a conjecture of Terwilliger.
Keywords:
q-Onsager algebra
Alternating central extension
Alternating generators
PBW basis
Tensor factorisation
17B37
17B67
81R50
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