13 papers
Quantum Groups and Bounded Symmetric Domains
S. Sinel'shchikov, L. Vaksman
Recent results of the authors on quantum bounded symmetric domains and quantum Harish-Chandra modules are expounded.
A Quantum Analogue of the Bernstein Functor
S. Sinel'shchikov, A. Stolin, L. Vaksman
We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological…
Quantum matrix ball: the Bergman kernel
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
In our preprint q-alg/9703005 q-analogues of bounded symmetric domains were defined to be homogeneous spaces of the associated quantum groups. The investigation of a simplest among…
Quantum matrix ball: differential and integral calculi
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
We have introduced q-analogues of bounded symmetric domains in our work q-alg/9703005. Given the simplest ones among those, the works q-alg/9603012 and math.QA/9803110 announce the…
q-Analogue of the Berezin quantization method
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
We use Berezin's quantization procedure to obtain a formal -invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators…
On Function Theory in Quantum Disc: A q-Analogue of Berezin Transform
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
This work contains a proof of theorem 7.3 from math.QA/9808015. This theorem demonstrates the Berezin method to be applicable for producing a well known one-parameter deformation o…