2 Rational Modules and Polynomial Modules

In [14] Hemmer conjectures that the module of fixed points for the symmetric group Σm of a Specht module for Σn (with n > m), over a field of positive characteristic p, has a Specht series, when viewed as a Σn−mmodule. We provide a counterexample for each prime p. The examples have the same form for p ≥ 5 and we treat the cases p = 3 and p = 2 separately.

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