Representation Theory and Geometry of the Flag Variety (De Gruyter Studies in Mathematics 90) (2022. VIII, 128 S. 20 b/w tbl. 240 mm)

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.