Geodesic
Discrete Branching Laws for Minimal Holomorphic Representations
Jan Möllers1 ; Yoshiki Oshima2
1Dept. of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, U.S.A.
2Kavli IPMU (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan
Journal of Lie Theory, Tome 25 (2015) no. 4, pp. 949-983

Voir la notice de l'article provenant de la source Heldermann Verlag

We find the explicit branching laws for the restriction of minimal holomorphic representations to symmetric subgroups in the case where the restriction is discretely decomposable. For holomorphic pairs the minimal holomorphic representation decomposes into a direct sum of lowest weight representations which is made explicit. For non-holomorphic pairs the restriction is shown to be irreducible and identified with a known representation. We further study a conjecture by Kobayashi on the behaviour of associated varieties under restriction and confirm this conjecture in the setting of this paper.
Classification : 22E46
Mots-clés : Minimal representation, highest weight representation, branching law, discretely decomposable, associated variety

Jan Möllers  1   ; Yoshiki Oshima  2

1 Dept. of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, U.S.A.
2 Kavli IPMU (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan 
Jan Möllers; Yoshiki Oshima. Discrete Branching Laws for Minimal Holomorphic Representations. Journal of Lie Theory, Tome 25 (2015) no. 4, pp. 949-983. http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a1/
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     author = {Jan M\"ollers and Yoshiki Oshima},
     title = {Discrete {Branching} {Laws} for {Minimal} {Holomorphic} {Representations}},
     journal = {Journal of Lie Theory},
     pages = {949--983},
     year = {2015},
     volume = {25},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a1/}
}
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