Abstract
Let Supern[U [unk] V] be the nth homogeneous subspace of the supersymmetric algebra of U [unk] V, where U and V are Z2-graded vector spaces over a field K of characteristic zero. The actions of the general linear Lie superalgebras pl(U) and pl(V) span two finite-dimensional K-subalgebras B and [unk] of EndK(Supern[U [unk] V]) that are the centralizers of each other. Young—Capelli symmetrizers and Young—Capelli *-symmetrizers give rise to K-linear bases of B and [unk] containing orthogonal systems of idempotents; thus they yield complete decompositions of B and [unk] into minimal left and right ideals, respectively.
Keywords: polarization operators, symmetrized Young bitableaux, Lie superalgebras, representation theory, Capelli's identities
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Selected References
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- Brini A., Palareti A., Teolis A. G. Gordan-Capelli series in superalgebras. Proc Natl Acad Sci U S A. 1988 Mar;85(5):1330–1333. doi: 10.1073/pnas.85.5.1330. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Rota G. C., Stein J. A. Symbolic method in invariant theory. Proc Natl Acad Sci U S A. 1986 Feb;83(4):844–847. doi: 10.1073/pnas.83.4.844. [DOI] [PMC free article] [PubMed] [Google Scholar]