Weight conjectures for fusion systems on an extraspecial group

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.

19 pages, expanded version of Section 8 of arXiv:1810.01453

References in corpus (2)

• On the number of simple modules in a block of a finite group
• Weight conjectures for fusion systems