Weight conjectures for fusion systems on an extraspecial group

2025/05/07 by Kessar, Radha, Linckelmann, Markus, Lynd, Justin +1
#20C15 #20C20 #20C25 #20C34 #20D20 #20E25 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.04840

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 p³, 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.

Related

• Proving a conjecture for fusion systems on a class of groups
• Minimal characteristic bisets and finite groups realizing Ruiz-Viruel\n exotic fusion systems
• Weight conjectures for ℓ-compact groups and spetses
• Fusion systems related to polynomial representations of SL₂(q)
• Weight conjectures for Parker--Semeraro fusion systems