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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.
Quantum groups and non-commutative complex analysis
S. Sinel'shchikov, L. Vaksman
The maximum principle for holomirphic functions in the quantum ball is formulated. A proof can be found in [8] (see the bibliography).
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…
Lectures on q-analogues of Cartan domains and associated Harish-Chandra modules
L. Vaksman
This volume contains a mildly expanded version of lectures and talks at seminars and conferences, as well as review papers on subjects listed in the title of the volume. A great de…
Quantum matrix ball: the Cauchi-Szegö kernel and the Shilov boundary
L. Vaksman
This work produces a q-analogue of the Cauchi-Szegö integral representation that retrieves a holomorphic function in the matrix ball from its values on the Shilov boundary. Besides…
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…