Fusion systems related to polynomial representations of SL2(q)

Valentina Grazian; Chris Parker; Jason Semeraro; Martin Van Beek

doi:10.1112/jlms.70481

Fusion systems related to polynomial representations of SL₂(q)

Valentina Grazian
, Chris Parker
, Jason Semeraro
, Martin Van Beek^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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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 SL₂(q), which includes the Sylow p-subgroups of SL₃(q) and SL₄(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.

Original language	English
Article number	e70481
Number of pages	54
Journal	Journal of London Mathematical Society
Volume	113
Issue number	3
DOIs	https://doi.org/10.1112/jlms.70481
Publication status	Published - 5 Mar 2026

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title = "Fusion systems related to polynomial representations of SL2(q)",

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 SL2(q), which includes the Sylow p-subgroups of SL3(q) and SL4(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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T1 - Fusion systems related to polynomial representations of SL2(q)

AU - Grazian, Valentina

AU - Parker, Chris

AU - Semeraro, Jason

AU - Van Beek, Martin

PY - 2026/3/5

Y1 - 2026/3/5

N2 - 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 SL2(q), which includes the Sylow p-subgroups of SL3(q) and SL4(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.

AB - 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 SL2(q), which includes the Sylow p-subgroups of SL3(q) and SL4(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.

UR - https://londmathsoc.onlinelibrary.wiley.com/journal/14697750

UR - https://research.manchester.ac.uk/en/publications/fusion-systems-related-to-polynomial-representations-of-slsub2sub/

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JO - Journal of London Mathematical Society

JF - Journal of London Mathematical Society

IS - 3

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ER -

Fusion systems related to polynomial representations of SL2(q)

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Fusion systems related to polynomial representations of SL₂(q)