Degrees of irreducible characters of (𝐵,𝑁)-pairs of types 𝐸₆ and 𝐸₇

Abstract

Let G be a finite (B, N)-pair whose Coxeter system is of type E 6 {E_6} or E 7 {E_7} . Let 1 B G 1_B^G be the permutation character of the action of G on the left cosets of the Borel subgroup B in G. In this paper we give the character degrees of the irreducible constituents of 1 B G 1_B^G .