<i>An Invitation to Representation Theory </i>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.<div><br></div><div><div>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.</div><div><br></div><div>With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first intr
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Expanding on lectures given at the LMS Autumn Algebra School 2020, this text gives a guided tour of modern developments in algebra and representation theory. It includes many worked examples and applications, providing graduate students and researchers...
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The primary goal of these lectures is to introduce a beginner to the finite¿ dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs,...
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Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book gives a comprehensive account of constructible and perverse sheaves on complex algebraic varieties,...
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