In this thesis, we prove that in the embedding of the Drinfeld double Dsln in the quantum torus algebra Dg, there are certain subsets of vertices such that
the embedding of the rescaled Chevalley generators ei 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.
Permanent URL for this record: https://lbezone.hkust.edu.hk/bib/991012980418003412