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arXiv · 2412.06670

Orthogonal bases for two-parameter quantum groups

Ian Martin·Alexander Tsymbaliuk
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Abstract

In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ in classical types, as used in our earlier work arXiv:2407.01450. Following the ideas of Leclerc and Clark-Hill-Wang, 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.

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BibTeXRIS

Ian Martin, Alexander Tsymbaliuk. 2024-12-09. Orthogonal bases for two-parameter quantum groups. https://doi.org/10.4171/qt%2F247

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