15 citations · 52 across the 13 of their papers we have counts for
13 papers
Fock Representations and Quantum Matrices
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
In this paper we study the Fock representation of a certain -algebra which appears naturally in the framework of quantum group theory. It is also a generalization of the twisted…
q-Analogues for Green functions for powers of the invariant Laplacian in the unit disc
D. Shklyarov
In a recent work of J. Peetre and M. Englius explicit formulae were obtained for Green functions of the powers of the Möbius-invariant Laplace operator in the unit disc. In the pre…
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…