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Flag Varieties: An Interplay of Geometry, Combinatorics, and Representation Theory: Second Edition
Justin Brown
Flag varieties are important geometric objects. Because of their richness in geometry, combinatorics, and representation theory, flag varieties may be described as an interplay of all three of these fields. This book gives a detailed account of this interplay. In the second edition, two recent results on Schubert varieties in the Grassmannian have been added. 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.