REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: We give a brief overview of quantum Weyl algebras and explain how some of them can be constructed using twisted tensor products defined via R-matrices. Building on this approach, quantum analogs of Weyl algebras are formed for several homogeneous spaces using both R-matrices and solutions to reflection equations. We discuss how these quantum Weyl algebras interact nicely with related quantized enveloping algebras in terms of module structures and embeddings. This talk is based on joint work with Hadi Salmasian and Siddhartha Sahi.