54 research outputs found
On the Shintani zeta function for the space of binary tri-Hermitian forms
In this paper, we consider the most non-split parabolic D_4 type
prehomogeneous vector space. The vector space is an analogue of the space of
Hermitian forms. We determine the principal part of the zeta function
Prehomogeneous vector spaces and ergodic theory III
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
Prehomogeneous vector spaces and field extensions III
In this paper, we determine the rational orbit decomposition for two
prehomogeneous vector spaces associated with the simple group of type G_2
On equivariant maps related to the space of pairs of exceptional Jordan algebras
Let be the exceptional Jordan algebra and . We construct an equivariant map from to
defined by
homogeneous polynomials of degree such that if is a generic point,
then the image of is the structure constant of the isotope of
corresponding to . We also give an alternative way to define the isotope
corresponding to a generic point of by an equivariant map from
to the space of trilinear forms.Comment: 10 page
On the GIT stratification of prehomogeneous vector spaces I
We determine the set which parametrizes the GIT stratification for four
prehomogeneous vector spaces in this paper
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