20 research outputs found
A Difference Version of Nori's Theorem
We consider (Frobenius) difference equations over (F_q(s,t), phi) where phi
fixes t and acts on F_q(s) as the Frobenius endomorphism. We prove that every
semisimple, simply-connected linear algebraic group G defined over F_q can be
realized as a difference Galois group over F_{q^i}(s,t) for some i in N. The
proof uses upper and lower bounds on the Galois group scheme of a Frobenius
difference equation that are developed in this paper. The result can be seen as
a difference analogue of Nori's Theorem which states that G(F_q) occurs as
(finite) Galois group over F_q(s).Comment: 29 page
The Fuchsian differential equation of the square lattice Ising model susceptibility
Using an expansion method in the variables that appear in the
-dimensional integrals representing the -particle contribution to the
Ising square lattice model susceptibility , we generate a long series of
coefficients for the 3-particle contribution , using a
polynomial time algorithm. We give the Fuchsian differential equation of order
seven for that reproduces all the terms of our long series. An
analysis of the properties of this Fuchsian differential equation is performed.Comment: 15 pages, no figures, submitted to J. Phys.
Connected Linear Groups as Differential Galois Groups
this paper we give a proof of the followin
and
In this paper we give a proof of the following THEOREM 1.1. Let C be an algebraically closed field of characteristic zero, G a connected linear algebraic group defined o�er C, and k a differential field containing C as its field of constants and of finite, nonzero transcendenc
Solvable-by-finite groups as differential Galois groups
We prove the inverse problem of differential Galois theory over the differential field k=C(x), where C is an algebraic closed field of characteristic zero, for linear algebraic groups G over CC with a solvable identity component G°. We show that for any k-irreducible principal homogeneous space V for G, the derivation d/dx of k can be extended on k(V) in such a way that k(V) is a Picard-Vessiot extension of k with Galois group G. The proof is constructive up to the finite embedding problem of classicalGalois theory over C(x)