An Invitation to Representation Theory offers an introduction to groups and their
representations suitable for undergraduates. In this book the ubiquitous symmetric group and
its natural action on polynomials are used as a gateway to representation theory. The subject
of representation theory is one of the most connected in mathematics with applications to
group theory geometry number theory and combinatorics as well as physics and chemistry. It
can however be daunting for beginners and inaccessible to undergraduates. The symmetric group
and its natural action on polynomial spaces provide a rich yet accessible model to study
serving as a prototype for other groups and their representations. This book uses this key
example to motivate the subject developing the notions of groups and group representations
concurrently. With prerequisites limited to a solid grounding in linear algebra this book can
serve as a first introduction to representation theory at the undergraduate level for instance
in a topics class or a reading course. A substantial amount of content is presented in over 250
exercises with complete solutions making it well-suited for guided study.
