Journal of Lie Theory 17 (2007), No. 1, 063--072
Copyright Heldermann Verlag 2007
Decomposition of a Tensor Product of a Higher Symplectic Spinor Module and the Defining Representation of sp(2n, C)
Svatopluk Krysl
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 73 Praha 8 - Karlín, Czech Republic
krysl@karlin.mff.cuni.cz
[Abstract-pdf]
\def\p{{\frak p}} \def\s{{\frak s}} \def\C{{\Bbb C}} Let $L(\lambda)$ be the irreducible highest weight $\s\p(2n,\C)$-module with a highest weight $\lambda$, such that $L(\lambda)$ is an infinite dimensional module with bounded multiplicities, and let $F(\varpi_1)$ be the defining representation of $\s\p(2n,\C)$. In this article, the tensor product $L(\lambda)\otimes F(\varpi_1)$ is explicitly decomposed into irreducible summands. This decomposition may be used in order to define some invariant first order differential operators for metaplectic structures.
Keywords: Symplectic spinors, harmonic spinors, Kostant's spinors, tensor products, decomposition of tensor products, modules with bounded multiplicities, Kac-Wakimoto formula.
MSC: 17B10; 17B81, 22E47
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