Geodesic
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.

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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 
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     author = {S. Krysl },
     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},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a3/}
}
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S. 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/JLT_2007_17_1_JLT_2007_17_1_a3/