Kac-Moody Groups, Their Flag Varieties & Representation Theory

Science & Math

Kumar, Shrawan

Kumar, S.

Mathematics

Birkhauser

Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings―definitions, properties and examples―to cutting edge research.

Frobenius Splitting Methods in Geometry and Representation Theory (Progress in Mathematics, 231)

Brion, Michel

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.

In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.\nBook Description\nThis book gives a complete proof of the Verlinde formula and of its connection to generalized theta functions.

Conformal Blocks, Generalized Theta Functions and the Verlinde Formula (New Mathematical Monographs, Series Number 42)

Cambridge University Press

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.

Kac-Moody Groups, their Flag Varieties and Representation Theory (Progress in Mathematics)

The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of the book would give a comprehensive introduction of these topics to graduate students and researchers.

Vector Bundles on Curves - New Directions: Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in ... 1995 (Lecture Notes in Mathematics, 1649)

Springer

See the best price to sell, buy, or rent books by Kumar, Shrawan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Kumar, Shrawan

See the best price to sell, buy, or rent books by Kumar, Shrawan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Kac-Moody Groups, Their Flag Varieties & Representation Theory

Frobenius Splitting Methods in Geometry and Representation Theory (Progress in Mathematics, 231)

Kac-Moody Groups, Their Flag Varieties & Representation Theory

Conformal Blocks, Generalized Theta Functions and the Verlinde Formula (New Mathematical Monographs, Series Number 42)

Kac-Moody Groups, their Flag Varieties and Representation Theory (Progress in Mathematics)

Vector Bundles on Curves - New Directions: Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in ... 1995 (Lecture Notes in Mathematics, 1649)