2025/02/22 by Song, Yanli
#11F72 #19K35 #19K56 #58B34 #58J20 #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2502.16100
Let G be a semi-simple real Lie group of real rank one and Γ be a discrete subgroup in G such that Γ\backslash G has finite volume. We introduce a new group C^*-algebra C^*r(G, Γ), which provides a natural framework for defining index classes of Dirac-type operators on the locally symmetirc space Γ\backslash G /K. We show that Dirac operators define elements in the K-theory of C^*r(G, Γ) and use Hecke correspondences to study their Lefschetz numbers. Our main result is an explicit formula for the Lefschetz number of Hecke operators.