Lie Algebras and Their Representations

by Kang, Seok-Jin; Kim, Myung-Hwan; Lee, Insok

• ISBN13: 9780821805121
• ISBN10: 0821805126
• Format: Hardcover
• Copyright: 1996-04-01
• Publisher: Amer Mathematical Society

Summary

This book contains the refereed proceedings of the symposium on Lie algebras and representation theory which was held at Seoul National University (Korea) in January 1995. The symposium was sponsored by the Global Analysis Research Center of Seoul National University. Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area. Consequently, this book can serve both as an introduction to various aspects of the theory of Lie algebras and their representations and as a good reference work for further research.

Table of Contents

Preface	vii
Commuting Actions---A Tale of Two Groups	1	(46)
Georgia Benkart
Lie Theory over Commutative Rings and Lifting Invariant Forms	47	(10)
Ben Cox
Polynomial Representations of Frobenius Kernels of GL2	57	(12)
Stephen R. Doty
Daniel K. Nakano
Karl M. Peters
Homological Topics in the Representation Theory of Restricted Lie Algebras	69	(52)
Jorg Feldvoss
An Exposition of Generalized Kac-Moody Algebras	121	(40)
Elizabeth Jurisich
Root Multiplicities of Graded Lie Algebras	161	(16)
Seok-Jin Kang
Similarity of Crystal Bases	177	(10)
Masaki Kashiwara
Some Topics on the Representation Theory of Generalized Kac-Moody Algebras	187	(14)
Satoshi Naito
Complexity and Support Varieties for Finite Dimensional Algebras	201	(18)
Daniel K. Nakano
Quasi-particle Structure in Solvable Vertex Models	219
Atsushi Nakayashiki