# Flag Varieties

## An Interplay of Geometry, Combinatorics, and Representation Theory

Part of the Texts and Readings in Mathematics book series (volume 53)

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Part of the Texts and Readings in Mathematics book series (volume 53)

Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.

- DOI https://doi.org/10.1007/978-93-86279-41-5
- Copyright Information Hindustan Book Agency (India) 2009
- Publisher Name Hindustan Book Agency, Gurgaon
- eBook Packages Mathematics and Statistics
- Print ISBN 978-81-85931-92-0
- Online ISBN 978-93-86279-41-5
- Series Print ISSN 2366-8717
- Series Online ISSN 2366-8725
- Buy this book on publisher's site