AG Lie-Gruppen: A. Sasaki

Datum: 13-01-2020Zeit: 14:15 – 16:45Ort: Übungsraum Ü2, Cauerstr. 11, Erlangen

Visible actions and geometric criteria for multiplicity-freeness of representations of Heisenberg groups

Vortragende: Atsumu Sasaki, Tokai University
Veranstalter: Karl-Hermann Neeb

Abstract:
The notion of strongly visible actions on complex manifolds has been introduced by T. Kobayashi (2004, 2005) to give an unified explanation of multiplicity-freeness property of representations of Lie groups which are realized in holomorphic sections of Hermitian holomorphic vector bundles (Propagation theorem of multiplicity-freeness property for holomorphic vector bundles). Many examples of strongly visible actions has been found in connection with multiplicity-free representations. Then, we expect that multiplicity-free representations realized in holomorphic sections have strongly visible actions on the base spaces. Recently, the classification problems of strongly visible actions are solved in various setting such as Hermitian symmetric spaces, flag varieties, linear spaces, nilpotent orbits and reductive complex homogeneous spaces. In this talk, we give a classification of strongly visible actions on complex Heisenberg homogeneous spaces. Moreover, as an application, we give a new geometric criterion for the quasi-regular representation of Heisenberg group to be multiplicity-free by strongly visible actions

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Details

Datum:
13-01-2020
Zeit:
14:15 – 16:45
Ort:

Übungsraum Ü2, Cauerstr. 11, Erlangen

Veranstaltungskategorien:
LIE-Gruppen