Covariant projective representations of Hilbert–Lie groups / Neeb, Karl-Hermann (Rights reserved)

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Title:: Journal für die reine und angewandte Mathematik

Publication:: Berlin: de Gruyter

Note:: Gesehen am 06.09.2018; 90!URL-Änderung(09-12-02);355!URL-Ä(30-01-12)

Scope:: Online-Ressource

ISSN:: 1435-5345

ZDB-ID:: 1468592-9

Keywords:: Angewandte Mathematik ; Mathematik ; Zeitschrift

Classification:: Mathematik

Collection:: Mathematik

Copyright:: Rights reserved

Accessibility:: Eingeschränkter Zugang mit Nutzungsbeschränkungen

Title:: Journal für die reine und angewandte Mathematik

Publication:: Berlin: de Gruyter

Note:: Gesehen am 06.09.2018; 90!URL-Änderung(09-12-02);355!URL-Ä(30-01-12)

Scope:: Online-Ressource

ISSN:: 1435-5345

ZDB-ID:: 1468592-9

Keywords:: Angewandte Mathematik ; Mathematik ; Zeitschrift

Classification:: Mathematik

Collection:: Mathematik

Copyright:: Rights reserved

Accessibility:: Eingeschränkter Zugang mit Nutzungsbeschränkungen

Article

Author:: Neeb, Karl-Hermann; Russo, Francesco G.

Title:: Covariant projective representations of Hilbert–Lie groups

Publication:: Berlin: de Gruyter, 2025

Language:: English

Information:: Abstract: Hilbert–Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. In this paper, we study unitary representations of these groups from various perspectives. First, we address norm-continuous, also called bounded, representations. These are well known for simple groups, but the general picture is more complicated. Our first main result is a characterization of the discrete decomposability of all bounded representations in terms of boundedness of the set of coroots. We also show that bounded representations of type II and III exist if the set of coroots is unbounded. Second, we use covariance with respect to a one-parameter group of automorphisms to implement some regularity. Here we develop some perturbation theory based on half-Lie groups that reduces matters to the case where a “maximal torus” is fixed, so that compatible weight decompositions can be studied. Third, we extend the context to projective representations which are covariant for a one-parameter group of automorphisms. Here important families of representations arise from “bounded extremal weights”, and for these, the corresponding central extensions can be determined explicitly, together with all one-parameter groups for which a covariant extension exists.

Scope:: Online-Ressource

Note:: Kein Open Access; Archivierung/Langzeitarchivierung gewährleistet

Classification:: Mathematik; Sonstiges

URN:: urn:nbn:de:101:1-2503010518211.700380542522

Collection:: Mathematik; Sonstiges

Copyright:: Rights reserved

Accessibility:: Eingeschränkter Zugang mit Nutzungsbeschränkungen

Author:: Neeb, Karl-Hermann; Russo, Francesco G.

Title:: Covariant projective representations of Hilbert–Lie groups

Publication:: Berlin: de Gruyter, 2025

Language:: English

Information:: Abstract: Hilbert–Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. In this paper, we study unitary representations of these groups from various perspectives. First, we address norm-continuous, also called bounded, representations. These are well known for simple groups, but the general picture is more complicated. Our first main result is a characterization of the discrete decomposability of all bounded representations in terms of boundedness of the set of coroots. We also show that bounded representations of type II and III exist if the set of coroots is unbounded. Second, we use covariance with respect to a one-parameter group of automorphisms to implement some regularity. Here we develop some perturbation theory based on half-Lie groups that reduces matters to the case where a “maximal torus” is fixed, so that compatible weight decompositions can be studied. Third, we extend the context to projective representations which are covariant for a one-parameter group of automorphisms. Here important families of representations arise from “bounded extremal weights”, and for these, the corresponding central extensions can be determined explicitly, together with all one-parameter groups for which a covariant extension exists.

Scope:: Online-Ressource

Note:: Kein Open Access; Archivierung/Langzeitarchivierung gewährleistet

Classification:: Mathematik; Sonstiges

URN:: urn:nbn:de:101:1-2503010518211.700380542522

Collection:: Mathematik; Sonstiges

Copyright:: Rights reserved

Accessibility:: Eingeschränkter Zugang mit Nutzungsbeschränkungen

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Typical Lipschitz images of rectifiable metric spaces / Bate, David (CC BY)
On κ-solutions and\break canonical neighborhoods in 4d Ricci flow / Haslhofer, Robert (Rights reserved)
On Vafa–Witten equations over Kähler manifolds / Chen, Xuemiao (Rights reserved)
Frontmatter (Rights reserved)
Quadratic differentials as stability conditions: Collapsing subsurfaces / Barbieri, Anna (Rights reserved)
The theory of F-rational signature / Smirnov, Ilya (Rights reserved)
Morse index bound of simple closed geodesics on 2-spheres and strong Morse inequalities / Ko, Dongyeong (Rights reserved)
A functorial approach to rank functions on triangulated categories / Conde, Teresa (CC BY)
Bergman kernel functions associated to measures supported on totally real submanifolds / Marinescu, George (Rights reserved)
Homology of configuration spaces of surfaces modulo an odd prime / Bianchi, Andrea (Rights reserved)
Logarithmic Gromov–Witten theory and double ramification cycles / Ranganathan, Dhruv (CC BY)
Multi-localized time-symmetric initial data for the Einstein vacuum equations / Anderson, John (Rights reserved)
Khovanov homology and exotic surfaces in the 4-ball / Hayden, Kyle (Rights reserved)
Irregular loci in the Emerton–Gee stack for GL 2 / Bellovin, Rebecca (Rights reserved)
The distribution of Manin’s iterated integrals of modular forms / Matthes, Nils (Rights reserved)
Endoscopy on SL 2 -eigenvarieties / Johansson, Christian (Rights reserved)
Isolated hypersurface singularities, spectral invariants, and quantum cohomology / Kawamoto, Yusuke (Rights reserved)
Ding stability and Kähler–Einstein metrics on manifolds with big anticanonical class / Dervan, Ruadhaí (Rights reserved)
Bounds on Cheeger–Gromov invariants and simplicial complexity of triangulated manifolds / Lim, Geunho (Rights reserved)
Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms. The high-dimensional case / Druet, Olivier (Rights reserved)
Good functions, measures, and the Kleinbock–Tomanov conjecture / Beresnevich, Victor (Rights reserved)
New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows / Frączek, Krzysztof (Rights reserved)
Lipschitz regularity of sub-elliptic harmonic maps into CAT (0) space / Assimos, Renan (Rights reserved)

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