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Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics.This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields.

This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12-13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, representations of quantum groups, and related topics.