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This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation
Kac-Moody Groups, their Flag Varieties and Representation Theory
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"Most of these topics appear here for the first time in book form. Many of them are interesting even in the classical case of semi-simple algebraic groups. Some
Affine Flag Varieties and Quantum Symmetric Pairs
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The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the qu
Kac-Moody Groups, their Flag Varieties and Representation Theory
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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 whi
Cohomology of Vector Bundles and Syzygies
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The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, a