The zeta functions of complexes from PGL(3): A representation-theoretic approach

Ming-Hsuan Kang*, Wen Ching Winnie Li, Chian Jen Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The zeta function attached to a finite complex X Γ arising from the Bruhat-Tits building for PGL 3 (F) was studied in [KL], where a closed form expression was obtained by a combinatorial argument. This identity can be rephrased using operators on vertices, edges, and directed chambers of X Γ . In this paper we re-establish the zeta identity from a different aspect by analyzing the eigenvalues of these operators using representation theory. As a byproduct, we obtain equivalent criteria for a Ramanujan complex in terms of the eigenvalues of the operators on vertices, edges, and directed chambers, respectively.

Original languageEnglish
Pages (from-to)335-348
Number of pages14
JournalIsrael Journal of Mathematics
Volume177
Issue number1
DOIs
StatePublished - 3 Sep 2010

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