Character stacks are PORC count

2022/03/09 by Nick Bridger, Bridger, Nick, Masoud Kamgarpour +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2203.04521

openalex publication_date 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key ingredients in the proof are Lusztig's Jordan decomposition of complex characters and Deriziotis's results on genus numbers of finite reductive groups. As a consequence of our main theorem, we obtain an expression for the E-polynomial of the character stack.

Cited by

• The sparsity of character tables over finite reductive groups and its additive analogue

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