Abstract The main aim of this article is to show that normalised standard intertwining operator between induced representations p -adic groups, at a very specific point evaluation, has an arithmetic origin. This result applications Eisenstein cohomology and the special values automorphic L -functions.

Let P be an induced hereditary property and L(P) denote the class of all graphs that satisfy the property P locally. The purpose of the present paper is to describe the minimal forbidden subgraphs of L(P) and the structure of local properties. Moreover, we prove that L(P) is irreducible for any hereditary property P. c © 2001 Elsevier Science B.V. All rights reserved.

Let P be a family of graphs. A graph G is said to satisfy a property P locally if G[N (v)]∈P for every v∈V (G). The class of graphs that satis6es the property P locally will be denoted by L(P) and we shall call such a class a local property. Let P be a hereditary property. A graph is said to be maximal with respect to a hereditary property P (shortly P-maximal) if it belongs to P and none of it...