A Natural Orthogonal Basis of Eigenfunctions of the Hecke Algebra Acting on Cayley Graphs

Abstract

Abstract.This paper discusses the representation of the Hecke algebra of GL2(F<?) on a class of Cayley graphs and gives a natural construction of an orthogonal basis of simultaneous eigenfunctions whose eigenvalues are the SotoAndrade Sums.

On Eigenvalues Related to Finite Poincaré Planes

“…is called the finite Poincaré plane. From [1], [2], [4], [7], we have the following facts: 1. G = GL 2 (F q ) acts on H q by linear transformation:…”

“…Using character sums, Evans [2] constructed an orthogonal basis of V that diagonalizes all the adjacency matrices. Kuang [4], using group representation theory, also constructed such an orthogonal basis. This paper will also compare these two bases.…”