# zbMATH — the first resource for mathematics

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].
##### MSC:
 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