From the 1 of 7 linked papers with an AI index.
7 papers
Ascending chains of irreducible lattices, bi-reversible automata and affine arithmetic groups
Pierre-Emmanuel Caprace, Justin Vast
The paper constructs infinite ascending chains of irreducible lattices in products of homogeneous trees and defines bi‑reversible automata whose associated groups have prescribed f…
The type I dichotomy for two-step nilpotent locally compact groups
Pierre-Emmanuel Caprace, Max Carter
We address the type I dichotomy for two-step nilpotent locally compact groups. Invoking work of Baggett-Kleppner, we characterize the closed points of the unitary dual of such a gr…
On the Howe--Moore property for automorphism groups of buildings
Andreas Thom, Pierre-Emmanuel Caprace
Let be a closed type-preserving subgroup of the automorphism group of a thick locally finite building of finite rank, and assume that acts Weyl-transitively. We prove t…
Fractal anti-tori
Pierre-Emmanuel Caprace, Justin Vast
Let be a group acting properly and cocompactly on the product of two trees and . An anti-torus is a non-periodic flat plane in that is the convex h…
On the self-similarity of rational power series with matrix coefficients
Pierre-Emmanuel Caprace, Justin Vast
Let be a prime, let be an integer and be the algebra of square matrices of size over the field of order . Let be polynomials…
Center-preserving irreducible representations of finite groups
Pierre-Emmanuel Caprace, Geoffrey Janssens, François Thilmany
Given finite groups , a representation of is called center-preserving on if the only elements of that become central under are those that were alrea…