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Orthogonal bases for two-parameter quantum groups
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DOI：10.4171/qt/247.png)
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In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups U-r,U-s(g) in classical types, as used in Martin-Tsymbaliuk [SIGMA 21 (2025), paper no. 064]. Following the ideas of Leclerc [Math. Z. 246 (2004), no. 4, 691-732] and Clark-Hill-Wang [Quantum Topol. 7 (2016), no. 3, 553-638], we introduce the two-parameter shuffle algebra and relate it to the subalgebras above. We then use the combinatorics of dominant Lyndon words to establish the main results.
Keyword:
quantum groups
shuffle algebras
Lyndon words
PBW bases
