[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′~).
Disciplines :
Mathematics
Author, co-author :
GUERIN, Clément ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Liu, Gang; Université de Lorraine- Institut Elie Cartan > Mathématiques > Maître de Conférences
Merino, Allan; National University of Singapore > Mathematics > Research assistant
External co-authors :
yes
Language :
English
Title :
Dual pairs in the Pin-group and duality for the corresponding spinorial representation
Alternative titles :
[fr] Paires duales dans le groupe Pin et dualité pour la représentation spinorielle correspondante
Publication date :
23 July 2021
Journal title :
Algebras and Representation Theory
ISSN :
1386-923X
eISSN :
1572-9079
Publisher :
Springer, Dordrecht, Netherlands
Volume :
24
Issue :
6
Pages :
1625–1640
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR11405402 - Analysis And Geometry Of Low-dimensional Manifolds, 2016 (01/09/2017-28/02/2021) - Jean-marc Schlenker
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