On the combinatorics of cluster realization of quantum groups

Abstract

In this thesis, we prove that in the embedding of the Drinfeld double Dsl_n in the quantum torus algebra D_g, there are certain subsets of vertices such that the embedding of the rescaled Chevalley generators e_i of the Drinfeld double remains polynomial under mutations at those vertices. We also describe a quantum analogue of the Lusztig coordinates for different reduced words of the longest element when the semisimple Lie algebra is of type A₃. Using this we show that the embedding of the Drinfeld double is independent of the choice of reduced word of the longest element for types A, D, and E.

Date of Award	2021
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Ivan Chi Ho IP (Supervisor)