Geodesic
Decomposition of a Tensor Product of a Higher Symplectic Spinor Module and the Defining Representation of sp(2n, C)
Svatopluk Krysl1
1Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 73 Praha 8 - Karlín, Czech Republic
Journal of Lie Theory, Tome 17 (2007) no. 1, pp. 63-72

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\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.
Classification : 17B10, 17B81, 22E47
Mots-clés : Symplectic spinors, harmonic spinors, Kostant's spinors, tensor products, decomposition of tensor products, modules with bounded multiplicities, Kac-Wakimoto formula

Svatopluk Krysl  1

1 Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 73 Praha 8 - Karlín, Czech Republic 
Svatopluk Krysl. Decomposition of a Tensor Product of a Higher Symplectic Spinor Module and the Defining Representation of sp(2n, C). Journal of Lie Theory, Tome 17 (2007) no. 1, pp. 63-72. http://geodesic.mathdoc.fr/item/JOLT_2007_17_1_a3/
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     title = {Decomposition of a {Tensor} {Product} of a {Higher} {Symplectic} {Spinor} {Module} and the {Defining} {Representation} of sp(2n, {C)}},
     journal = {Journal of Lie Theory},
     pages = {63--72},
     year = {2007},
     volume = {17},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_1_a3/}
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