TY - BOOK ID - 5339498 TI - Kac-Moody groups, their flag varieties, and representation theory PY - 2002 VL - v. 204 SN - 0817642277 3764342277 1461266149 1461201055 9780817642273 PB - Boston : Birkhäuser, DB - UniCat KW - Kac-Moody algebras. KW - Representations of groups. KW - Flag manifolds. KW - Kac-Moody, Algèbres de KW - Représentations de groupes KW - Variétés de drapeaux (Géométrie) KW - Representations of groups KW - Flag manifolds KW - Kac-Moody algebras KW - Kac-Moody, Algèbres de KW - Représentations de groupes KW - Variétés de drapeaux (Géométrie) KW - Algebraic topology. KW - Topological groups. KW - Lie groups. KW - Algebra. KW - Algebraic geometry. KW - Group theory. KW - Algebraic Topology. KW - Topological Groups, Lie Groups. KW - Algebraic Geometry. KW - Group Theory and Generalizations. KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Algebraic geometry KW - Geometry KW - Mathematics KW - Mathematical analysis KW - Groups, Lie KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Groups, Topological KW - Continuous groups KW - Topology UR - https://www.unicat.be/uniCat?func=search&query=sysid:5339498 AB - Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge­ bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan­ dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g. ER -