An exotic Springer correspondence for F₄

2025/08/19 by Jonas Antor, Antor, Jonas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2508.14199

openalex publication_date 2025/08/19 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We investigate the structure of the `exotic nilcone' of F<sub>4</sub> which is defined by exploiting certain characteristic two phenomena. We show that there are finitely many orbits on this nilcone and construct an associated Springer correspondence. Further to that, we show that all corresponding `exotic Springer fibers' admit an affine paving. We also deduce from this a geometric classification of certain simple modules for the affine Hecke algebra with unequal parameters of type F₄.

Citations

• Geometric realizations of affine Hecke algebras with unequal parameters
• Classification of unipotent representations of simple p-adic groups,II

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• Exotic symmetric space over a finite field, I
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