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Kentaro Hara

Tokyo University of Science, Japan

Title: Deformation quantization of symmetric Kähler manifolds

Biography

Biography: Kentaro Hara

Abstract

A deformation quantization with separation of variables is one of wellknown quantizations of Kahler manifolds. Explicit expressions of the quantization for CN , CPN and CHN were known. We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric Kahler manifold. CN , CPN and CHN were locally symmetric Kahler manifolds and Riemann surfaces are also locally symmetric Kahler manifolds. It is not easy to solve the recurrence relations but some are solvable. We found a deformation quantization with separation of variables for Riemann surfaces.