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On a distinguished class of infinite dimensional representations of \(\mathfrak{sp}(2n,\mathbb C)\). (English) Zbl 1100.15014
Slovák, Jan (ed.) et al., The proceedings of the 24th winter school “Geometry and physics”, Srní, Czech Republic, January 17–24, 2004. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 75, 269-277 (2005).
Summary: We show how a tensor product of an infinite dimensional representation within a certain distinguished class of infinite dimensional irreducible representations of \({\mathfrak {sp}}(2n,\mathbb C)\) with the defining representation decomposes. Further we prove a theorem on complete reducibility of a \(k\)-fold tensor product of the defining representation (tensored) with a member of the distinguished class.
For the entire collection see [Zbl 1074.53001].
15A66 Clifford algebras, spinors
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
15A69 Multilinear algebra, tensor calculus
53C27 Spin and Spin\({}^c\) geometry