Preface This volume contains the refereed proceedings of the Symposium on Lie Al- gebras and Representation Theory which was held at Seoul National University, Seoul, Korea, from January 23 to 27, 1995. The Symposium was sponsored by the Global Analysis Research Center of Seoul National University. Over the past 30 years, we have observed many exciting developments in diverse areas of the theory of Lie algebras and their representations. The following are some of the most remarkable achievements during this period. 1. Kac-Moody algebras were introduced and numerous interesting applications have been discovered in the areas of number theory, combinatorics, and mathematical physics. 2. Combinatorial methods were brouglit into the representation theory of Lie algebras. 3. Classification of finite dimensional simple Lie algebras over algebraically closed fields of characteristic p 7 was completed. The purpose of this symposium was to bring together the ideas from the above- mentioned areas of the theory of Lie algebras and their representations and discuss the recent developments in these rapidly growing fields of research. It also served as a good opportunity for young Korean mathematicians to get acquainted with the theory of Lie algebras and their representations, and stimulated the research ac- tivities in the Korean mathematical community. The following topics were covered during the Symposium. - Lie algebras and combinatorics - Crystal bases for quantum groups - Quantum groups and solvable lattice models - Modular Lie algebras - Infinite dimensional Lie algebras In this volume the readers will find several excellent expository articles as well as research papers containing many significant new results on the subject. So, this volume will serve both as a kind of introduction to the various aspects of the theory of Lie algebras and their representations and as a good reference for further research. Some articles will be very interesting to physicists as well as mathematicians. We would like to thank all the participants of the Symposium for their ex- cellent lectures and contributed papers. We also thank our graduate students Jin Hong, Hye-Jin Ku, Jae-Hoon Kwon, Byeong-Kweon Oh, and Jihun Park for their assistance during the Symposium. Special thanks should be given to Professor vii
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