Ebook: 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- and infinite-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.

Discusses the structure and singularities of the flag variety of complex reductive Lie groups and its connections to the representation theory of such groups and real forms coverage including, finite-and infinite-dimensional representation theory.