Differential calculi on some quantum prehomogeneous vector spaces

Relative invariants of some 2-simple prehomogeneous vector spaces

In this paper, we shall construct explicitly irreducible relative invariants of two 2-simple prehomogeneous vector spaces. Together with a preprint by the same authors, this completes the list of all relative invariants of regular 2-simple prehomogeneous vector spaces of type I.

Diierential Calculi on Quantum Vector Spaces with Hecke-type Relations

From a vector space V equipped with a Yang-Baxter operator R one may form the r-symmetric algebra S R V = T V =hvw?R(vw)i, which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebra M R V = T (End(V))=hf g ? R(f g)R ?1 i. In the case when R satisses a Hecke-type identity R 2 = (1?q)R+q, we construct a diierential calculus R V for S R V which agrees with tha...

Prehomogeneous Vector Spaces and Field Extensions Ii

Free Divisors in Prehomogeneous Vector Spaces

We study linear free divisors, that is, free divisors arising as discriminants in prehomogeneous vector spaces, and in particular in quiver representation spaces. We give a characterization of the prehomogeneous vector spaces containing such linear free divisors. For reductive linear free divisors, we prove that the numbers of geometric and representation theoretic irreducible components coinci...

On Parameterizations of Rational Orbits of Some Forms of Prehomogeneous Vector Spaces

In this paper, we consider the structure of rational orbit of some prehomogeneous vector spaces originally motivated by Wright and Yukie. After we give a refinement of WrightYukie’s construction, we apply it to the inner forms of the D5 and E7 types. Parameterizations of reducible algebras for the cubic cases are included.