Dobrev V.K. Invariant Differential Operators, Volume 2: Quantum Groups

Walter de Gruyter GmbH, Berlin, Boston, 2017. — 409 p. — (De Gruyter Studies in Mathematical Physics 39) — ISBN10: 3110435438.This is volume 2 of our trilogy on invariant differential operators. In volume 1 we presented our canonical procedure for the construction of invariant differential operators and showed its application to the objects of the initial domain – noncompact semisimple Lie algebras and groups.
In volume 2 we show the application of our procedure to quantum groups. Similarly to the setting of volume 1 the main actors are in duality. Just as Lie algebras and Lie groups are in duality here the dual objects are the main two manifestations of quantum groups: quantum algebras and matrix quantum groups. Actually, quantum algebras typically are deformations of the universal enveloping algebras of semisimple Lie algebras. Analogously, matrix quantum groups typically are deformations of
spaces of functions over semisimple Lie groups.Quantum Groups and Quantum Algebras
Highest-Weight Modules over Quantum Algebras
Positive-Energy Representations of Noncompact Quantum Algebras
Duality for Quantum Groups
Invariant q-Difference Operators
Invariant q-Difference Operators Related to GLq(n)
q-Maxwell Equations Hierarchies