02558nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003500213245013200248260008200380300003400462336002600496337002600522338003600548347002400584490004000608506006600648520123700714650002101951650004001972650003302012650005302045856003202098856006602130225-180504CH-001817-320180504233001.0a fot ||| 0|cr nn mmmmamaa180504e20180525sz fot ||| 0|eng d a978303719681670a10.4171/1812doi ach0018173 7aPBP2bicssc a22-xxa28-xxa60-xx2msc1 aKosyak, Alexander V.,eauthor.10aRegular, Quasi-regular and Induced Representations of Infinite-dimensional Groupsh[electronic resource] /cAlexander V. Kosyak3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (587 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v291 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAlmost all harmonic analysis on locally compact groups is based on the existence (and uniqueness) of a Haar measure. Therefore, it is very natural to attempt a similar construction for non-locally compact groups. The essential idea is to replace the non-existing Haar measure on an infinite-dimensional group by a suitable quasi-invariant measure on an appropriate completion of the initial group or on the completion of a homogeneous space.
The aim of the book is a systematic development, by example, of noncommutative harmonic analysis on infinite-dimensional (non-locally compact) matrix groups. We generalize the notion of regular, quasi-regular and induced representations for arbitrary infinite-dimensional groups. The central idea to verify the irreducibility is the Ismagilov conjecture. We also extend the Kirillov orbit method for the group of upper triangular matrices of infinite order.
In order to make the content accessible to a wide audience of nonspecialists, the exposition is essentially self-contained and very few prerequisites are needed. The book is aimed at graduate and advanced undergraduate students, as well as mathematicians who wish an introduction to representations of infinite-dimensional groups.07aTopology2bicssc07aTopological groups, Lie groups2msc07aMeasure and integration2msc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/181423cover imageuhttps://www.ems-ph.org/img/books/kosyak_mini.jpg