Journal of Lie Theory 35 (2025), No. 3, 617--628
Copyright Heldermann Verlag 2025
Admissible Systems and Graded Hermitian Superspaces
Meng-Kiat Chuah
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
chuah@math.nthu.edu.tw
Rita Fioresi
(1) FaBiT, University of Bologna, Italy
(2) INFN, Sezione Bologna, Italy
rita.fioresi@unibo.it
Fabio Gavarini
(1) Dip. di Matematica, University of Rome ``Tor Vergata'', Roma, Italy
(2) Istituto Nazionale di Alta Matematica / GNSAGA, Roma, Italy
gavarini@mat.uniroma2.it
We introduce the notion of admissible systems for involutions on complex contragredient Lie superalgebras, and classify the involutions with admissible systems by circlings on extended Dynkin diagrams. We prove the graded Iwasawa decomposition of the symmetric pair (g, k) consisisting of the contragredient Lie superalgebra g and the fixed points of an involution. We also show the representability in the category of complex superspaces of the corresponding real symmetric superspace.
Keywords: Contragredient Lie superalgebras, involutions, admissible systems, real forms, Dynkin diagrams.
MSC: 17B20, 17B22, 17B40.
[ Fulltext-pdf (312 KB)] for subscribers only.