Dynamical degrees of affine-triangular automorphisms of affine spaces

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

Flat graphs based on affine spaces and affine symplectic spaces

Let AG(n,Fq) be the n-dimensional affine space over the finite field Fq. For 0 ≤ m ≤ n − 1, define a graph G whose vertex set is the set of all m-flats of AG(n,Fq), such that two vertices F1 and F2 are adjacent if dim(F1∨F2) = m+1, where F1∨F2 is the minimum flat containing both F1 and F2. Let ASG(2ν,Fq) be the 2ν-dimensional affine-symplectic space over Fq. Define a graph S (ν) whose vertex se...

The Automorphisms of Affine Fusion Rings

arose first in rational conformal field theory (RCFT) as an extremely useful expression for the dimensions of conformal blocks on a genus g surface with t punctures. Φ here is the finite set of ‘primary fields’. The matrix S comes from a representation of SL2(Z) defined by the chiral characters of the theory. Contrary to appearances, these numbers V (g) ⋆···⋆ will always be nonnegative integers...

Infinitesimal Affine Automorphisms of Symplectic Connections

Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic nilmanifold admitting a flat symplectic connection and an infinitesimal automorphism that is not symplectic. On a symplectic manifold (M,Ω), a symplectic connection is a torsion-free affine ...

ON POLYNOMIAL AUTOMORPHISMS OF AFFINE SPACESVladimir