Lectures On Representation Theory

This book is an expanded version of the lectures given at the NankaiMathematical Summer School in 1997. It provides an introduction to Lie groupsLie algebras an... » 

This book is an expanded version of the lectures given at the NankaiMathematical Summer School in 1997. It provides an introduction to Lie groupsLie algebras and their representations as well as a flavor of current researchfor graduate students who have no previous specialized knowledge ofrepresentation theory. It only assumes that the reader has a good knowledge ofundergraduate linear algebra.Parts IIII of the book provide relatively elementary material aboutrepresentation theory on finite groups and on compact Lie groups. A chapter onsimple groups of the Lie type has been added to the original notes so that thereader can have a complete picture of simple finite groups. Part IV presentssome advanced material on infinitedimensional representations of noncompactgroups. The last part of the notes touches on many important ideas of currentresearch such as orbit methods minimal representations and dual paircorrespondences which may serve as an introduction to the current research onrepresentation theory. «