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arXiv · 2405.14395

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

Jianhao Shen
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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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Jianhao Shen. 2026-04-15. Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type. https://arxiv.org/abs/2405.14395

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