Construction of irreducible relative invariant of the prehomogeneous vector space \((\text{SL}_5 {\times} \text{GL}_4,\Lambda^{2}({\mathbb C}^5)\otimes{\mathbb C}^4)\)
type: Item
instance of: scholarly article
title: Construction of irreducible relative invariant of the prehomogeneous vector space \((\text{SL}_5 {\times} \text{GL}_4,\Lambda^{2}({\mathbb C}^5)\otimes{\mathbb C}^4)\)
zbMATH Open document ID: 1027.11091
DOI: 10.1016/S0024-3795(02)00348-8
author: Katsutoshi Amano
author: Masaki Fujigami
author: Takeyoshi Kogiso
published in: Linear Algebra and its Applications
publication date: 2003-02-05T00:00:00Z
review text: The explicit construction of an irreducible relative invariant on a prehomogeneous vector space is a fundamental problem in the study of invariant theory. For almost all of the irreducible prehomogeneous vector spaces, they are already computed explicitly, but some are left as being unsolved problems. The prehomogeneous vector space \((\text{SL}_5\times \text{GL}_4, \Lambda^2\otimes \Lambda^1)\) is known as one of the difficult cases to compute. The authors of this paper construct the irreducible relative invariant of this prehomogeneous vector space. Their method is based on the construction of an equivariant surjection from \((\text{SL}_5\times \text{GL}_4, \Lambda^2\otimes \Lambda^1)\) to \((\text{GL}_4, 2\Lambda_1S^2 (\mathbb{C}^4))\). The irreducible relative invariant of the former prehomogeneous vector space is obtained as the composition of the surjection and the relative invariant of the latter prehomogeneous vector space.
Mathematics Subject Classification ID: 11S90
zbMATH DE Number: 1864742
zbMATH Keywords: irreducible relative invariant
zbMATH Keywords: prehomogeneous vector space
zbMATH Keywords: invariant theory
reviewed by: Masakazu Muro
MaRDI profile type: Publication
cites work: Construction of invariants
cites work: Invariants, nilpotent orbits, and prehomogeneous vector spaces
cites work: A classification of irreducible prehomogeneous vector spaces and their relative invariants
cites work: Quotients of some prehomogeneous vector spaces
description: scientific article; zbMATH DE number 1864742