Laurence Barker
Published 2018-09-28Version 1
For any characteristic zero coefficient field, an irreducible representation of a finite $p$-group can be assigned a Roquette $p$-group, called the genotype. This has already been done by Bouc and Kronstein in the special cases Q and C. A genetic invariant of an irrep is invariant under group isomorphism, change of coefficient field, Galois conjugation, and under suitable inductions from subquotients. It turns out that the genetic invariants are precisely the invariants of the genotype. We shall examine relationships between some genetic invariants and the genotype. As an application, we shall count Galois conjugacy classes of certain kinds of irreps.
On irreducible representations of discrete nilpotent groups
A simple counting argument of the irreducible representations of SU(N) on mixed product spaces
On commutations of derivatives and integrals of $\square$-irreducible representations for $p$-adic $\mathrm{GL}$
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