Bilinear forms on $\mathfrak{sl}_2$-modules and a hypergeometric identity

Details Bilinear forms on $\mathfrak{sl}_2$-modules and a hypergeometric identity Bilinear forms on $\mathfrak{sl}_2$-modules and a hypergeometric identity

2007-02-06

arxiv.org/abs/math/0702137v2

Mathematics

Representation Theory

Changed claims of new identity to references of known identity. Added reference to book by Klimyk and Vilenkin

Scientific paper

In this paper we study properties of a certain bilinear form on finite
dimensional $\mathfrak{sl}_2(\mathbb{R})$-modules, and how these properties
behave with respect to tensor products of modules. An attempt to determine the
signature of this form leads to an interesting identity for the hypergeometric
series ${}_3F_2$, which is known as the Karlsson-Minton identity.

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