2024/12/09 by Martin, Ian, Tsymbaliuk, Alexander
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2412.06670
In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups Ur,s(\mathfrakg) 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.