Episode 2777
Prehomogeneous vector space
Tue, 2024-Dec-10 00:30 UTC
Length - 1:47
Direct Link
Welcome to Random Wiki of the Day, your journey through Wikipedia’s vast and varied content, one random article at a time.
The random article for Tuesday, 10 December 2024 is Prehomogeneous vector space.
In mathematics, a prehomogeneous vector space (PVS) is a finite-dimensional vector space V together with a subgroup G of the general linear group GL(V) such that G has an open dense orbit in V. The term prehomogeneous vector space was introduced by Mikio Sato in 1970. These spaces have many applications in geometry, number theory and analysis, as well as representation theory. The irreducible PVS were classified first by Vinberg in his 1960 thesis in the special case when G is simple and later by Sato and Tatsuo Kimura in 1977 in the general case by means of a transformation known as "castling". They are subdivided into two types, according to whether the semisimple part of G acts prehomogeneously or not. If it doesn't then there is a homogeneous polynomial on V which is invariant under the semisimple part of G.
This recording reflects the Wikipedia text as of 00:30 UTC on Tuesday, 10 December 2024.
For the full current version of the article, see Prehomogeneous vector space on Wikipedia.
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