O'Reilly logo

Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

14

Inner products of characters

We establish some significant properties of characters in this chapter, and in particular we prove the striking result (Theorem 14.21) that if two imageG-modules have the same character then they are isomorphic. Also, we describe a method for decomposing a given imageG-module as a direct sum of imageG-submodules, using characters.

The proofs rely on an inner product involving the characters of a group, and we describe this first.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required