Representation Theory and Geometry of the Flag Variety

This comprehensive reference begins with a review of the basics followed by a presentation of flag varieties and finite-dimensional representations in classical types and subvarieties of flag varieties and their singularities. Associated varieties and characteristic cycles are covered as well and Kazhdan-Lusztig polynomials are treated. The coverage concludes with a discussion of pattern avoidance and singularities and some recent results on Springer fibers.