TY - JOUR
T1 - The zeta functions of complexes from PGL(3)
T2 - A representation-theoretic approach
AU - Kang, Ming-Hsuan
AU - Li, Wen Ching Winnie
AU - Wang, Chian Jen
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77956122847&partnerID=8YFLogxK
U2 - 10.1007/s11856-010-0049-2
DO - 10.1007/s11856-010-0049-2
M3 - Article
AN - SCOPUS:77956122847
SN - 0021-2172
VL - 177
SP - 335
EP - 348
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -