Products of characters and finite p-groups II

Abstract

Let p be a prime number. Let G be a finite p-group and $\chi \in Irr(G)$. Denote by $\bar{\chi }\in Irr(G)$ the complex conjugate of $\chi$. Assume that $\chi (1)=p^n$. We show that the number of distinct irreducible constituents of the product $\chi \bar{\chi }$ is at least $2n(p-1)+1$.

Submitted, 8 pages, see http://www.math.uiuc.edu/~adanbant