Berezin’s quantization on flag manifolds and spherical modules

Karabegov, Alexander

doi:10.1090/S0002-9947-98-02099-6

Berezin’s quantization on flag manifolds and spherical modules
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by Alexander V. Karabegov PDF

Trans. Amer. Math. Soc. 350 (1998), 1467-1479 Request permission

Abstract:

We show that the theory of spherical Harish-Chandra modules naturally gives rise to Berezin’s symbol quantization on generalized flag manifolds. It provides constructions of symbol algebras and of their representations for covariant and contravariant symbols, and also for symbols which so far have no explicit definition. For all these symbol algebras we give a general proof of the correspondence principle.

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