Unitarizing probability measures for representations of Virasoro algebra (Q1606246)

The purpose of this rich article is to work out explicitly a one-to-one correspondence between realizations of some representations of Virasoro algebra on a space of holomorphic square integrable functions and unitarizing probability measures satisfying an integration by parts formula. Two realizations are discussed in detail: the first based on Neretin polynomials in the context of Kirillov homogeneous space of univalent functions and the second based on an infinite-dimensional version of Berezin quantization scheme. See also [C. R. Math., Acad. Sci. Paris 334, 787-794 (2002; Zbl 1008.58025)].