Title
Minimal dimensions of Sym(n)- and Alt(n)-modules
Abstract
We present a new, natural notion of “modules with an additive dimension” covering at once the classical, finitary case as well as modules definable in an o-minimal or finite Morley rank setting. In this context, we fully identify the faithful Sym(n)- and Alt(n)-modules of least dimension, generalising a century-old result by Leonard Dickson and its more recent companions Ascher Wagner. We also discuss connections to permutation groups of finite Morley rank possessing a high degree of generic transitivity. This is joint work with Luis Jaime Corredor and Adrien Deloro.
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