Prehomogeneous Vector Spaces and Field Extensions Ii
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چکیده
منابع مشابه
COMPUTATION OF CHARACTER SUMS AND APPLICATIONS TO PREHOMOGENEOUS VECTOR SPACES 1 with an appendix ” L - FUNCTIONS OF PREHOMOGENEOUS VECTOR SPACES
For an arbitrary number field K with ring of integers OK , we prove an analogue over finite rings of the form OK/p of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where p is a big enough prime ideal of OK and m > 1. In the appendix, F. Sato gives an application of the Theorems 1.2 and 1.5 (and Theorems A, B, C in [4]) to the functiona...
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The purpose of this note is to give a short derivation of the finite field analogue of Sato’s functional equation for the zeta function associated with a prehomogeneous vector space (see [16]). We restrict ourselves to the case of a regular prehomogeneous vector space, however, we allow to twist our character sums by local systems associated to arbitrary representations of the component group o...
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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.
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For a number field K with ring of integers O K , we prove an analogue over finite rings of the form O K /P m of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where P is a big enough prime ideal of O K and m > 1. In the appendix, F. to the functional equation of L-functions of Dirichlet type associated with prehomogeneous vector spaces.
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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...
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