arXiv subjects
Publications and source records attributed to L. Vaksman.
Our previous work (math.QA/9808015) introduces the basic notions and announces some results on function theory in the quantum disc. The present paper establishes a relationship between those results and the quantum groups theory.
This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.
This work considers a formal deformation of the quantum disc (it is developed via an application of the Berezin method) and presents an explicit formula for this deformation.
A standard bicovariant differential calculus on a quantum matrix space ${\tt Mat}(m,n)_q$ is considered. The principal result of this work is in observing that the $U_q\frak{s}(\frak{gl}_m\times \frak{gl}_n))_q$ is in fact a $U_q\frak{sl}(m+n)$-module differential algebra.