Equivariant Polynomial Automorphisms of -representations

Nonlinear Equivariant Automorphisms

We show that the natural representation of SL 3 SL 5 SL 13 allows nonlinear equivariant automorphisms; more exactly, the group of polynomial au-tomorphisms on C 3 C 5 C 13 commuting with the simple SL 3 SL 5 SL 13-action is isomorphic to C n C. This is the rst example of a simple module with nonlinear equivariant automorphisms.

SL2-equivariant polynomial automorphisms of the binary forms

“galois” Automorphisms of Complex Reflection Groups

Let G be a complex reflection group and K its field of definition (the subfield of C generated by the reflection character). We show that Gal(K/Q) injects into the group A of outer automorphisms of G which preserve reflections, and that this injection with a few exceptions can be chosen such that it commutes with the Galois action on characters of G; further, replacing if needed K by an extensi...

Explicit Hilbert spaces for certain unipotent representations

Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P = L N be its Shilov boundary parabolic subgroup. This paper attaches an irreducible unitary representation of G to each of the (finitely many) L-orbits on n*. The Hilbert space of the representation consists of functions on the orbit which are square-integrable with respect to a certain L-equivariant...

Equivariant Embeddings of Trees into Hyperbolic Spaces

For every cardinal α ≥ 2 there are three complete constant curvature model manifolds of Hilbert dimension α: the sphere S, the Euclidean space E and the hyperbolic space H. Studying isometric actions on these spaces corresponds in the first case to studying orthogonal representations and in the second case to studying cohomology in degree one with orthogonal representations as coefficients. In ...