Pre homogeneous spaces and stratified Kahler spaces

Johannes Huebschmann

Description

Pre-homogeneous spaces and stratified Kahler spaces J. Huebschmann USTL, UFR de Mathematiques CNRS-UMR 8524 59655 Villeneuve d'Ascq Cedex, France Bielefeld July 22, 2007 1

• pre-homogeneous spaces


• homogeneous space


• kahler spaces


• g0-pre-homogeneous structure


• exotic stratified


• stratified kahler space


• lie group


• kahler space establishes

Sujets

• Homogeneous space
• Lie group

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 37
• Langue: English

Extrait

Pre-homogeneousspacesandstratified Ka¨hlerspaces J.Huebschmann USTL,UFRdeMathe´matiques CNRS-UMR8524 59655Villeneuved’AscqCe´dex,France [e-mail] BielefeldJuly22,2007 1

Abstract ArepresentationofareductiveLiegroupisapre-homogeneous spaceprovidedithasaZariski-openorbit.AstratifiedKa¨hler spaceisastratifiedsymplecticspacetogetherwithacomplexan- alyticstructurewhichiscompatiblewiththestratifiedsymplectic structure;inparticulareachstratumisaKa¨hlermanifoldinan obviousfashion.ThenotionofstratifiedKa¨hlerspaceestablishes anintimaterelationshipbetweennilpotentorbits,singularreduc- tion,invarianttheory,reductivedualpairs,Jordantriplesystems, symmetricdomains,andpre-homogeneousspaces.Thepurpose ofthetalkistoillustratethegeometryofstratifiedKa¨hlerspaces. ExamplesofstratifiedKa¨hlerspacesabound.Theclosureof aholomorphicnilpotentorbitcarriesanormalKa¨hlerstructure. SymplecticreductioncarriesaKa¨hlermanifoldtoanormalstrat- ifiedKa¨hlerspaceinsuchawaythatthesheafofgermsofpo- larizedfunctionscoincideswiththeordinarysheafofgermsof holomorphicfunctions.Projectivizationofholomorphicnilpo- tentorbitsyieldsexoticstratifiedKa¨hlerstructuresoncomplex projectivespacesandoncertaincomplexprojectivevarietiesin- cludingcomplexprojectivequadrics,Scorzavarietiesandtheir secantvarieties.Physicalexamplesarereducedspacesarising fromangularmomentum. Theappearanceofsingularitiesinclassicalphasespacesisthe ruleratherthantheexception.Whilewithincanonicalquantiza- tiontheimplementationofsingularitiesisfarfrombeingclearthe possibleimpactofclassicalphasespacesingularitiesonquantum problemscanbeexploredviaquantizationonstratifiedKa¨hler spaces. 2