Flag Varieties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Flag Varieties write by V Lakshmibai. This book was released on 2018-06-26. Flag Varieties available in PDF, EPUB and Kindle. This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.
Kac-Moody Groups, their Flag Varieties and Representation Theory
Kac-Moody Groups, their Flag Varieties and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Kac-Moody Groups, their Flag Varieties and Representation Theory write by Shrawan Kumar. This book was released on 2002-09-10. Kac-Moody Groups, their Flag Varieties and Representation Theory available in PDF, EPUB and Kindle. "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 appendices recall useful results from other areas, so the work may be considered self-contained, although some familiarity with semi-simple Lie algebras or algebraic groups is helpful. It is clear that this book is a valuable reference for all those interested in flag varieties and representation theory in the semi-simple or Kac-Moody case." —MATHEMATICAL REVIEWS "A lot of different topics are treated in this monumental work. . . . many of the topics of the book will be useful for those only interested in the finite-dimensional case. The book is self contained, but is on the level of advanced graduate students. . . . For the motivated reader who is willing to spend considerable time on the material, the book can be a gold mine. " —ZENTRALBLATT MATH
Kac-Moody Groups, their Flag Varieties and Representation Theory
Kac-Moody Groups, their Flag Varieties and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Kac-Moody Groups, their Flag Varieties and Representation Theory write by Shrawan Kumar. This book was released on 2012-12-06. Kac-Moody Groups, their Flag Varieties and Representation Theory available in PDF, EPUB and Kindle. 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.
Affine Flag Varieties and Quantum Symmetric Pairs
Affine Flag Varieties and Quantum Symmetric Pairs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Affine Flag Varieties and Quantum Symmetric Pairs write by Zhaobing Fan. This book was released on 2020-09-28. Affine Flag Varieties and Quantum Symmetric Pairs available in PDF, EPUB and Kindle. 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 quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Cohomology of Vector Bundles and Syzygies
Cohomology of Vector Bundles and Syzygies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cohomology of Vector Bundles and Syzygies write by Jerzy Weyman. This book was released on 2003-06-09. Cohomology of Vector Bundles and Syzygies available in PDF, EPUB and Kindle. 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, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.
