Download E-books Kac-Moody Groups, Their Flag Varieties & Representation Theory PDF

By S. Kumar

Kac-Moody Lie algebras nine have been brought within the mid-1960s independently by means of V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge­ bras which we discuss with because the finite case. the idea has passed through super advancements in a variety of instructions and connections with different parts abound, together with mathematical physics, loads in order that this thought has develop into a stan­ dard instrument in arithmetic. an in depth remedy of the Lie algebra point of the speculation are available in V. Kac's publication [Kac-90l This self-contained paintings treats the algebro-geometric and the topological elements of Kac-Moody conception from scratch. The emphasis is at the learn of the Kac-Moody teams nine and their flag forms XY, together with their particular building, and their purposes to the illustration idea of g. within the finite case, nine is not anything yet a semisimple Y simply-connected algebraic workforce and X is the flag style nine /Py for a parabolic subgroup p y C g.

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