Flag varieties are important geometric objects and their study
involves an interplay of geometry, combinatorics, and
representation theory. This book is a 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 Grassmann varieties,
flag varieties, and their Schubert subvarieties. Because of their
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. In this second edition, two recent
results on Schubert varieties in the Grassmannian have been added,
and some errors in the first edition corrected.
General
Imprint: |
Jainendra K Jain
|
Country of origin: |
India |
Release date: |
May 2018 |
Authors: |
V. Lakshmibai
• Justin Brown
|
Dimensions: |
229 x 152 x 25mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
325 |
Edition: |
2nd Revised edition |
ISBN-13: |
978-93-86-27970-5 |
Categories: |
Books
|
LSN: |
93-86-27970-3 |
Barcode: |
9789386279705 |
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