Prehomogeneous vector spaces and ergodic theory III
Representation Theory
2009-09-25 v1
Abstract
Let H_1=SL(5), H_2=SL(3), H=H_1 \times H_2. It is known that (G,V) is a prehomogeneous vector space (see [22], [26], [25], for the definition of prehomogeneous vector spaces). A non-constant polynomial \delta(x) on V is called a relative invariant polynomial if there exists a character \chi such that \delta(gx)=\chi(g)\delta(x). Such \delta(x) exists for our case and is essentially unique. So we define V^{ss}={x in V such that \delta(x) is not equal to 0}. For x in V_R^{ss}, let H_{x R+}^0 be the connected component of 1 in classical topology of the stabilizer H_{x R}. We will prove that if x in V_R^ss is "sufficiently irrational", H_{x R+}^0 H_Z is dense in H_R.
Keywords
Cite
@article{arxiv.math/9702220,
title = {Prehomogeneous vector spaces and ergodic theory III},
author = {Akihiko Yukie},
journal= {arXiv preprint arXiv:math/9702220},
year = {2009}
}