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arXiv · 2505.04840

Weight conjectures for fusion systems on an extraspecial group

Radha Kessar·Markus Linckelmann·Justin Lynd·Jason Semeraro
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Abstract

In a previous paper, we stated and motivated counting conjectures for fusion systems that are purely local analogues of several local-to-global conjectures in the modular representation theory of finite groups. Here we verify some of these conjectures for fusion systems on an extraspecial group of order $p^3$, which contain among them the Ruiz-Viruel exotic fusion systems at the prime $7$. As a byproduct we verify Robinson's ordinary weight conjecture for principal $p$-blocks of almost simple groups $G$ realizing such (nonconstrained) fusion systems.

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Radha Kessar, Markus Linckelmann, Justin Lynd, Jason Semeraro. 2025-05-07. Weight conjectures for fusion systems on an extraspecial group. https://doi.org/10.1017/s1446788725101390

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