Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups

Abstract

We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of automorphisms of certain non-commutaive rings of quotients coming from complex powers of quantum group generators; this is applied to explicit calculation of singular vectors in Verma modules over $U_{q}(\gtsl_{n+1})$. We finally give a definition of a $q-$connection with coefficients in a ring of skew polynomials and study the structure of quantum group modules twisted by a $q-$connection.

arXiv comment25 pages

References in corpus (1)

• Solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded modules

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