Kailash C. Misra

Vyjayanthi Chari

Jacob Greenstein

K. N. Raghavan

Sankaran Viswanath

This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, Riverside, CA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalizations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.

Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory

David Hernandez

Springer Nature

Prasad Senesi

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification, held on the occasion of Charis 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Charis significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

In Honor of Vyjayanthi Chari on the Occasion of Her 60th Birthday

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Brian J. Parshall

Daniel K. Nakano

This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

Pramod M. Achar

Dijana Jakelić

Milen Yakimov

This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics

Naihuan Jing

Yun Gao

Michael Lau

This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.

Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, March 2-7, 2008, Banff International Research Station, Banff, Canada

Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications

Brian Parshall

Daniel Ken Nakano

This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.

2009-2011 Southeastern Lie Theory Workshop Series : Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University : Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia : Finite and Algebraic Groups, June 1-4, 2011, University of Virginia

Recent Developments in Lie Algebras, Groups, and Representation Theory

James Lepowsky

Yi-Zhi Huang

Robert L. Wilson

The articles in this book are based on talks given at the international conference ""Lie algebras, vertex operator algebras and their applications"", in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twenty-first century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory. This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above.

International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays, May 17-21, 2005, North Carolina State University, Raleigh, North Carolina

Lie Algebras, Vertex Operator Algebras and Their Applications

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying 'center stage' in the theory of infinite dimensional Lie theory.

Representations of Affine and Quantum Affine Algebras and Their Applications, North Carolina State University, May 21-24, 1998

Recent Developments in Quantum Affine Algebras and Related Topics

Kailash C. Misra

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