Overview

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.

Full Product Details

Author:   Yiqiang Li ,  Changlong Zhong
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470477271

ISBN 10:   1470477270
Pages:   195
Publication Date:   10 June 2026
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Forthcoming
Availability:   Not yet available  
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Table of Contents

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

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Author Information

Yiqiang Li, University at Buffalo, State University of New York, NY. Changlong Zhong, University at Albany, State University of New York, NY.

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