Lectures on Kac-Moody groups (Q2707768)

The article under review is based on a series of lectures given by the author at Sophia University in Tokyo in 2000. The aim of this lecture note is to give an introduction to Kac-Moody groups mainly for the first year graduate students or the last year undergraduate students. Topics are carefully selected and well-organized in relatively short pages. We list the contents in the following: Section 0. Preface. Section 1. Tits systems. Section 2. Ordered sets and amalgamated sum. Section 3. Kac-Moody algebras. Section 4. Root systems and Weyl groups. Section 5. Kac-Moody groups. Section 6. Appendices. References are given and divided into two parts: 16 text books related to the topics in this note (5 are in Japanese) and 17 research papers are mentioned in the note.NEWLINENEWLINENEWLINEThe results shown in Sections 1-4 are combined in Section 5 to give the main results of this note. Here we give the titles of the subsections of Section 5. (5.1) Chevalley bases. (5.2) Kac-Moody groups. (5.3) Existence of Tits systems. (5.4) Birkhoff decompositions. (5.5) The structure of \(U^{YPm}\). (5.6) Group presentations. (5.7) Global Gauss decomposition.NEWLINENEWLINENEWLINEThe note is intended to be self-contained and proofs are given in a leisurely manner, so it is not hard to follow the arguments. If translated into English this note will have a wide range of readers as a handy introduction to Kac-Moody groups.