2023/08/12 by Snowden, Andrew · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2308.06648
In previous work with Harman, we introduced a new class of representations for an oligomorphic group G, depending on an auxiliary piece of data called a measure. In this paper, we look at this theory when G is the symmetry group of the Cantor set. We show that G admits exactly two measures μ and ν. The representation theory of (G, μ) is the linearization of the category of F2-vector spaces, studied in recent work of the author and closely connected to work of Kuhn and Kovács. The representation theory of (G, ν) is the linearization of the category of vector spaces over the Boolean semi-ring (or, equivalently, the correspondence category), studied by Bouc--Thévenaz. The latter case yields an important counterexample in the general theory.