Abstract' Homomorphisms of Split Kac-Moody Groups.

Intro -- Contents -- Introduction -- Acknowledgements -- Chapter 1. The objects: Kac-Moody groups, root data and Tits buildings -- 1.1. Kac-Moody groups and Tits functors -- 1.2. Root data -- 1.3. Tits buildings -- 1.4. Twin root data and twin buildings: a short dictionary -- Chapter 2. Basic tools from geometric group theory -- 2.1. CAT(0) geometry -- 2.2. Rigidity of algebraic-group-actions on trees -- Chapter 3. Kac-Moody groups and algebraic groups -- 3.1. Bounded subgroups -- 3.2. Adjoint representation of Tits functors -- 3.3. A few facts from the theory of algebraic groups -- Chapter 4. Isomorphisms of Kac-Moody groups: an overview -- 4.1. The isomorphism theorem -- 4.2. Diagonalizable subgroups and their centralizers -- 4.3. Completely reducible subgroups and their centralizers -- 4.4. Basic recognition of the ground field -- 4.5. Detecting rank one subgroups of Kac-Moody groups -- 4.6. Images of diagonalizable subgroups under Kac-Moody group isomorphisms -- 4.7. A technical auxiliary to the isomorphism theorem -- Chapter 5. Isomorphisms of Kac-Moody groups in characteristic zero -- 5.1. Rigidity of SL[sub(2)](Q)-actions on CAT(0) polyhedral complexes -- 5.2. Homomorphisms of Chevalley groups over Q to Kac-Moody groups -- 5.3. Regularity of diagonalizable subgroups -- 5.4. Proof of the isomorphism theorem -- Chapter 6. Isomorphisms of Kac-Moody groups in positive characteristic -- 6.1. On bounded subgroups of Kac-Moody groups -- 6.2. Homomorphisms of certain algebraic groups to Kac-Moody groups -- 6.3. Images of certain small subgroups under Kac-Moody group isomorphisms -- 6.4. Proof of the isomorphism theorem -- Chapter 7. Homomorphisms of Kac-Moody groups to algebraic groups -- 7.1. The non-linearity theorem -- 7.2. A combinatorial characterization of affine Coxeter groups -- 7.3. On infinite root systems.

7.4. Proof of the non-linearity theorem -- Chapter 8. Unitary forms of Kac-Moody groups -- 8.1. Introduction -- 8.2. Definitions -- 8.3. Isomorphisms of unitary forms -- 8.4. Non-linearity -- Bibliography -- Index -- A -- B -- C -- D -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W.

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