A new prehomogeneous vector space of characteristic p
type: Item
instance of: scholarly article
title: A new prehomogeneous vector space of characteristic p
zbMATH Open document ID: 0645.14023
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: This paper deals with a new type of prehomogeneous vector space of characteristic \(p\) which does not appear in the case of characteristic zero. The author has shown the following theorem: Let K be an algebraically closed field of characteristic 3. Let \(\Lambda_ 1, \Lambda_ 2, \Lambda_ 3\) denote all the fundamental dominant weights of GL(4). Then the K-dimension of the irreducible GL(4)-module V with the highest weight \(\Lambda_ 1+\Lambda_ 2\) is equal to 16, and it is denoted by V(16). In this paper, the following results are proved. (1) \((GL(4),\Lambda_ 1+\Lambda_ 2,V(16))\) is a regular irreducible prehomogeneous vector space. The degree of its irreducible relative invariant is 8, the associated character is \(\chi (g)=(\det (g))\) 6. (2) There exist only one 6-dimensional GL(4)-orbit and one 9-dimensional GL(4)-orbit in V(16). When \(m=7, 8\) or \(1\leq m\leq 5\), there are no m- dimensional GL(4)-orbits.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 4051792
zbMATH Keywords: regular irreducible prehomogeneous vector space
author: Zhi-Jie Chen
reviewed by: Masakazu Muro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4051792