Geodesic
The Left-Regular Representation of a Super Lie Group
Gijs M. Tuynman1
1Dép. de Mathématiques, Faculté des Sciences et Technologies, Université de Lille, 59655 Villeneuve d'Ascq, France
Journal of Lie Theory, Tome 29 (2019) no. 1, pp. 1-78

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Zbl

With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will show that weakening the definition of a super Hilbert space (by allowing the super scalar product to be non-homogeneous, not just even) will allow the left-regular representation of all (connected) super Lie groups to be super unitary (with an adapted definition). Along the way I will introduce a (super) metric on a supermanifold that will allow me to define super and non-super scalar products on function spaces.
Classification : 58A50, 22E99, 57S20
Mots-clés : Super manifolds, super Lie groups, regular representation, super unitary representation

Gijs M. Tuynman  1

1 Dép. de Mathématiques, Faculté des Sciences et Technologies, Université de Lille, 59655 Villeneuve d'Ascq, France 
Gijs M. Tuynman. The Left-Regular Representation of a Super Lie Group. Journal of Lie Theory, Tome 29 (2019) no. 1, pp. 1-78. http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a0/
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     title = {The {Left-Regular} {Representation} of a {Super} {Lie} {Group}},
     journal = {Journal of Lie Theory},
     pages = {1--78},
     year = {2019},
     volume = {29},
     number = {1},
     zbl = {1418.58003},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a0/}
}
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