Abstract
We consider symmetric pairs of Lie superalgebras and introduce a graded Harish-Chandra homomorphism. Generalising results of Harish-Chandra and V. Kac, M. Gorelik, we prove that, assuming reductivity, its image is a certain explicit filtered subalgebra J(\( \mathfrak{a} \)) of the Weyl invariants on a Cartan subspace whose associated graded gr J(\( \mathfrak{a} \)) is the image of Chevalley’s restriction map on symmetric invariants. In contrast to the known cases, J(\( \mathfrak{a} \)) is in general not isomorphic to gr J(\( \mathfrak{a} \)).
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This research was supported by the Leibniz group, SFB/Transregio 12, SPP 1388, and IRTG 1133 grants, funded by Deutsche Forschungsgemeinschaft (DFG).
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Alldridge, A. The Harish-Chandra isomorphism for reductive symmetric superpairs. Transformation Groups 17, 889–919 (2012). https://doi.org/10.1007/s00031-012-9200-y
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DOI: https://doi.org/10.1007/s00031-012-9200-y