# Lectures on Gaussian Integral Operators and Classical Groups

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*Yurii A. Neretin*

A publication of the European Mathematical Society

This book is an elementary self-contained introduction to
some constructions of representation theory and related topics of
differential geometry and analysis.

Topics covered include the theory of various Fourier-like integral
operators such as Segal–Bargmann transforms, Gaussian integral
operators in \(L^2\) and in the Fock space, integral
operators with theta-kernels, the geometry of real and
\(p\)-adic classical groups and symmetric spaces.

The heart of the book is the Weil representation of the symplectic group
(real and complex realizations, relations with theta-functions and modular
forms, \(p\)-adic and adelic constructions) and representations in
Hilbert spaces of holomorphic functions of several complex variables.

This book is addressed to graduate students and researchers in
representation theory, differential geometry, and operator
theory. Prerequisites are standard university courses in linear
algebra, functional analysis, and complex analysis.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in representation theory, differential geometry, and operator theory.