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June 2009 A classification of reductive prehomogeneous vector spaces with trivial representation free
Masaya Ouchi
Tsukuba J. Math. 33(1): 177-188 (June 2009). DOI: 10.21099/tkbjm/1251833213

Abstract

In this paper, we classify $k$-simple prehomogeneous vector spaces of type $(GL_{1}^{l}\times G_{1}\times \cdots \times G_{k},\rho _{1}^{(1)}\otimes \cdots \otimes \rho _{k}^{(1)}+ \cdots + \rho_{1}^{(l)}\otimes \cdots \otimes \rho _{k}^{(l)})$ where for any $i,j$, each $\rho _{j}^{(i)}$ is a nontrivial irreducible representation of a simple algebraic group $G_{j}$(i.e., $\rho _{j}^{(i)}\neq 1$) with $k\ge 3$ and $l\ge 2$ under full scalar multiplications. We consider everything over the complex number field $\mathbb {C}$.

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Masaya Ouchi. "A classification of reductive prehomogeneous vector spaces with trivial representation free." Tsukuba J. Math. 33 (1) 177 - 188, June 2009. https://doi.org/10.21099/tkbjm/1251833213

Information

Published: June 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1191.20042
MathSciNet: MR2553844
Digital Object Identifier: 10.21099/tkbjm/1251833213

Rights: Copyright © 2009 University of Tsukuba, Institute of Mathematics

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Vol.33 • No. 1 • June 2009
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