On modular representations of p-solvable groups

MINI-COURSE: p-MODULAR REPRESENTATIONS OF p-ADIC GROUPS

1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...

Good Representations and Solvable Groups

The purpose of this paper is to provide a characterization of solvable linear algebraic groups in terms of a geometric property of representations. Representations with a related property played an important role in the proof of the equivariant Riemann-Roch theorem [EG2]. In that paper, we constructed representations with that property (which we call freely good) for the group of upper triangul...

Resolutions of p-Modular TQFT’s and Representations of Symmetric Groups

Quantization and Representations of Solvable Lie Groups

Introduction. In this note, we will announce a characterization of a connected, simply connected Type I solvable Lie group, G, and present a complete description of the set of all unitary equivalence classes of irreducible unitary representations of G together with a construction of an irreducible representation in each equivalence class. This result subsumes the results previously obtained on ...

Modular Representations of Symmetric Groups

Over the last few weeks, we have seen lots of things in representation theory—we began by looking at an onslaught of examples to see explicitly what representations look like, we discussed character theory and looked at character tables, we talked about representations from a module-theoretic perspective, and then we saw how we can model the representation theory of the symmetric group via the ...