02372nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003200221245010800253260008200361300003400443336002600477337002600503338003600529347002400565490006100589506006600650520099800716650003401714650004001748650005501788650002501843650003101868856003201899856006701931126-110225CH-001817-320110225234510.0a fot ||| 0|cr nn mmmmamaa110225e20110225sz fot ||| 0|eng d a978303719580270a10.4171/0802doi ach0018173 7aPBFD2bicssc a22-xxa32-xxa47-xxa53-xx2msc1 aNeretin, Yurii A.,eauthor.10aLectures on Gaussian Integral Operators and Classical Groupsh[electronic resource] /cYurii A. Neretin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (571 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis 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 as Segalâ€“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.
The book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. The reader is supposed to be familiar with standard university courses in linear algebra, functional analysis, and complex analysis.07aGroups & group theory2bicssc07aTopological groups, Lie groups2msc07aSeveral complex variables and analytic spaces2msc07aOperator theory2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/080423cover imageuhttps://www.ems-ph.org/img/books/neretin_mini.jpg