Representation Theory

Front Cover
Cambridge University Press, Feb 5, 2015 - Mathematics - 191 pages
This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background. An important highlight of this book is an innovative treatment of the Robinson-Schensted-Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of Schur-Weyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Chapter_01
1
Chapter_02
32
Chapter_03
51
Chapter_04
70
Chapter_05
96
Chapter_06
141
Hints and Solutions to Selected Exercises
160
Suggestions for Further Reading
182
References
185
Index
189
Copyright

Other editions - View all

Common terms and phrases

About the author (2015)

Amritanshu Prasad is a Professor of Mathematics at the Institute of Mathematical Sciences (IMSc), Chennai. Before joining IMSc in 2003, he was a CRM-CICMA fellow at the Centre de Recherche Mathématiques, a Canadian centre for research in the fundamental sciences located at the Université de Montréal. He has held visiting positions at the Max Planck Institute for Mathematics in Bonn and the Institut des Hautes Études Scientifiques in Bur-sur-Yvette, near Paris. He has been an Associate of the Indian Academy of Sciences (2005-2010) and is a winner of the Young Scientist Medal of the Indian National Science Academy (2010). He completed his PhD under the supervision of Robert E. Kottwitz at the University of Chicago (2001). He holds a Masters degree from the University of Chicago (1996) and a Bachelor's degree in Statistics from the Indian Statistical Institute, Kolkata (1995). He has taught undergraduate and graduate students in the United States, Canada, and India. His mathematical interests include representation theory, number theory, harmonic analysis and combinatorics.

Bibliographic information