Sam K. Miller

activity

20242026

collaborators

5 papers

math.GR2026

Non-orientable representation spheres

Sam K. Miller

For any finite group, we pose the following question: given an irreducible real representation, is the associated representation sphere non-orientable if and only if the representa…

math.GR2026

The fusion-stable tom Dieck homomorphism

Sam K. Miller

Tornehave and Yalçin proved that the tom Dieck homomorphism, which sends a virtual real representation to a unit of the Burnside ring, is surjective for any $p$ -group $S$ . We prove…

math.RT2026

The classification of integral endotrivial complexes

Juan Omar Gómez, Sam K. Miller

We describe the group of endotrivial complexes, i.e., the Picard group, of the derived category of permutation modules for a finite group over a commutative Noetherian ring. As a r…

math.RT2025

The Euler characteristic of an endotrivial complex

Nadia Mazza, Sam K. Miller

Let $G$ be a finite group and $k$ a field of prime characteristic $p$ . We examine the Lefschetz homomorphism $Λ : E_{k} (G) \to O (T (k G))$ from the group of endotrivial comple…

math.RT2024

On endosplit $p$ -permutation resolutions and Broué's conjecture for $p$ -solvable groups

Sam K. Miller

Endosplit $p$ -permutation resolutions play an instrumental role in verifying Broué's abelian defect group conjecture in numerous cases. We give a new characterization of all endosp…

Non-orientable representation spheres

The fusion-stable tom Dieck homomorphism

The classification of integral endotrivial complexes

The Euler characteristic of an endotrivial complex

On endosplit p-permutation resolutions and Broué's conjecture for p-solvable groups

On endosplit $p$ -permutation resolutions and Broué's conjecture for $p$ -solvable groups