This volume contains the proceedings of the AMS Special Session on Representation Theory and Flag Varieties, held at the AMS Sectional Meeting at SUNY Buffalo on September 9-10, 2023. Representation theory, which originated with Frobenius's work on group representations in the late 19th century, explores symmetries in mathematics and natural sciences. It has evolved into a broad field since then. Its geometric approach, leverages flag and Nakajima quiver varieties, produces significant results such as the resolution of the Kazhdan-Lusztig conjecture, connects to disciplines such as enumerative geometry, algebraic geometry, and mathematical physics, and in return reveals hidden structures within these varieties. This volume compiles recent advancements in representation theory and flag/quiver variety geometry, offering original research and expository articles. Contributions include work on generalized Shubert calculus, quantum $K$-theory of semi-infinite flag variety, research on geometry of Springer fibers and their variants, combinatorial model for quiver varieties, and results on $G$-connections in the geometric Langlands program, providing fresh insights and methodologies.
Mee Seong Im, Shifra Reif, and Vera Serganova,
The Grothendieck ring of the periplectic Lie supergroup and supersymmetric
functions;
Julianna S. Tymoczko, Divided difference operators for partial flag
varieties;
Daniele Rosso and Neil Saunders, Exotic Spaltenstein varieties;
Rebecca Goldin and Martha Precup, Minimal semisimple Hessenberg schemes;
Drew Meyer, On the pure dimensionality of Spaltenstein varieties: A family of
counterexamples;
Daniel S. Sage, Connections on the projective line whose differential Galois
groups are as large as possible;
Li Li, Nakajima's quiver varieties and triangular bases of bipartitle cluster
algebras;
Changlong Zhong, Elliptic Schubert clases and the Poincare duality;
Yiqiang Li, Quasi-split symmetric pairs of type A and Steinberg varieties of
classical type, II. Constructible functions
Yiqiang Li, University at Buffalo, State University of New York, NY.
Changlong Zhong, University at Albany, State University of New York, NY.
