Vaksman L. Quantum theory of bounded symmetric domains

Objects: quantum analogues of bounded symmetric domains. Goals: producing a quantum theory of bounded symmetric domains. Methods: methods of representation theory of real reductive groups, quantum group theory, and theory of unitary dilations for compressions. New theoretical results: the author was first in producing differential calculi over quantum analogues of function algebras in bounded symmetric domains, in finding an explicit form of the invariant integral, in obtaining q-analogues for Bergman and Cauchi-Szego inte-gral representations. Employment: non-commutative complex analysis, non-commutative harmonic analysis, rigorously solv-able problems of modern mathematical physics.