Reference : Dual pairs in the Pin-group and duality for the corresponding spinorial representation
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/39954
Dual pairs in the Pin-group and duality for the corresponding spinorial representation
English
[fr] Paires duales dans le groupe Pin et dualité pour la représentation spinorielle correspondante
Guerin, Clément mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Liu, Gang mailto [Université de Lorraine- Institut Elie Cartan > Mathématiques > > Maître de Conférences]
Merino, Allan mailto [National University of Singapore > Mathematics > > Research assistant]
23-Jul-2019
22
No
[en] dual pairs ; duality ; Pin group
[en] In this paper, we give a complete picture of Howe correspondence for the setting (O(E,b),Pin(E,b),Π), where O(E,b) is an orthogonal group (real or complex), Pin(E,b) is the two-fold Pin-covering of O(E,b), and Π is the spinorial representation of Pin(E,b). More precisely, for a dual pair (G,G′) in O(E,b), we determine explicitly the nature of its preimages (G̃,G′~) in Pin(E,b), and prove that apart from some exceptions, (G̃,G′~) is always a dual pair in Pin(E,b); then we establish the Howe correspondence for Π with respect to (G̃,G′~).
Researchers
http://hdl.handle.net/10993/39954
https://arxiv.org/abs/1907.09093
FnR ; FNR11405402 > Jean-Marc Schlenker > AGoLoM > Analysis and Geometry of Low-dimensional Manifolds > 01/09/2017 > 31/08/2020 > 2016

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