Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type

2024/05/23 by Shen, Jianhao
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.14395

Abstract

For the Tits building B(G) of a finite group of Lie type G(Fq), we study the edge zeta function, which enumerates edge-geodesic cycles in the 1-skeleton. We show that every nonzero edge eigenvalue becomes a power of q after raising to a bounded exponent k depending on the type of G. The proof is uniform across types using a Hecke algebra approach. This extends previous results for type A and for oppositeness graphs to the full edge-geodesic setting and all finite groups of Lie type.

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