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Abstract: this paper, k is a field of characteristic zero. In parts one and two [25], [23], we consider cases (2), (5), (6), (7) in the Sato--Kimura classification [19]. In this part, we consider the prehomogeneous vector space G = GL(5) \Theta GL(3); V = (Update)
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...Theta GL(7) V = 3 k 7 , 3) G = GL(2n) V = 2 k 2n . For the definition of prehomogeneous vector spaces, see [7] 11] or [10]. The classification of irreducible regular prehomogeneous vector spaces is known [7] For any algebraic group G, we denote the connected...
...(2) n = 2, 4) 8) 9) 11) 12) 15) m = 2, 17) 26) 28) because stabilizers of points in V ss do not satisfy Condition 4. In [26], 25] 27] we considered cases (3) 5) 6) 7) 10) In [28] we consider all the other applicable cases except for the cases (1)...
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Yukie, A. Prehomogeneous vector spaces and ergodic theory I. To appear in Duke Math. J. http://citeseer.ist.psu.edu/39075.html More
@misc{ yukie-prehomogeneous,
author = "A. Yukie",
title = "Prehomogeneous vector spaces and ergodic theory",
text = "Yukie, A. Prehomogeneous vector spaces and ergodic theory I. To appear
in Duke Math. J.",
url = "citeseer.ist.psu.edu/39075.html" }
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