On irreducible representations of free group

TL;DR

This paper demonstrates that for certain free group representations, tensor products are typically irreducible, and constructs examples of irreducible boundary realizations with infinite-dimensional fibers.

Contribution

It establishes generic irreducibility of tensor products in a class of free group representations and constructs infinite-dimensional boundary realizations.

Findings

Tensor products are generically irreducible for certain free group representations.

Existence of irreducible boundary realizations with infinite-dimensional fibers.

Provides new insights into the structure of free group representations.

Abstract

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.