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

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

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The zeta function attached to a finite complex XΓ arising from the Bruhat-Tits building for PGL3(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 XΓ. 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 (US)
Pages (from-to)335-348
Number of pages14
JournalIsrael Journal of Mathematics
Volume177
Issue number1
DOIs
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'The zeta functions of complexes from PGL(3): A representation-theoretic approach'. Together they form a unique fingerprint.

Cite this