On the polynomiality conjecture of cluster realization of quantum groups

2023/02/08 by Ip, Ivan Chi-Ho, Ye, Jeff York
#13F60 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2302.04020

Abstract

In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra O_q(X) to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.

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