Let q be a power of a fixed prime p. We classify up to isomorphism all simple saturated fusion systems on a certain class of p-groups constructed from the polynomial representations of SL(2,q), which includes the Sylow p-subgroups of GL(3,q) and Sp(4,q) as special cases. The resulting list includes all Clelland-Parker fusion systems, a simple exotic fusion system discovered by Henke-Shpectorov, and a new infinite family of exotic examples.
Fusion systems related to polynomial representations of SL(2,q)
Grazian V.;
2026
Abstract
Let q be a power of a fixed prime p. We classify up to isomorphism all simple saturated fusion systems on a certain class of p-groups constructed from the polynomial representations of SL(2,q), which includes the Sylow p-subgroups of GL(3,q) and Sp(4,q) as special cases. The resulting list includes all Clelland-Parker fusion systems, a simple exotic fusion system discovered by Henke-Shpectorov, and a new infinite family of exotic examples.
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