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Zbl 1141.14030
Vallès, Jean
Hyperdeterminant of an $SL_{2}$-homomorphism. (Hyperdéterminant d'un $SL_{2}$-homomorphisme.) (French)
[J] Ann. Math. Blaise Pascal 15, No. 1, 81-86 (2008). ISSN 1259-1734

Summary: Let $A_{1}, \cdots ,A_{s} (s \geq 3)$ be non-trivial $SL_{2}(\Bbb C)$-modules with dimensions $n_{1} + 1 \geq \cdots \geq n_{s} + 1$ (such that $n_{1} = n_{2}+ \cdots +n_{s})$ and $\phi \in \cal {L}(A_{2} \otimes \cdots \otimes A_{s},A_{1}^{*})$ an $SL_{2}(\Bbb C)$-homomorphism. We show that the hyperdeterminant of $\phi $ is null except if the modules $A_{i}$ are irreducibles and the homomorphism is the multiplication of homogeneous polynomials with two variables.

MSC 2000:: *14M12 Determinantal varieties
14L30 Group actions on varieties or schemes
14J60 Vector bundles on surfaces and higher-order varieties
16D99 Modules, bimodules and ideals (assoc. rings and algebras)

Keywords: hyperdeterminant; Steiner bundles; $SL_{2}$ modules

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