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Book DetailsContemporary MathematicsVolume: 695; 2017; 274 ppMSC: Primary 17; 18; 32; 81
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana.
Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by YiZhi Huang summarizing some major open problems in these areas, in particular as they pertain to twodimensional conformal field theory.
ReadershipGraduate students and research mathematicians interested in representation theory, vertex algebras, conformal field theory and related areas.

Table of Contents

Articles

Darlayne Addabbo and Maarten Bergvelt — Generalizations of $Q$systems and orthogonal polynomials from representation theory

Dražen Adamović and Antun Milas — Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory

Ling Bao and Lisa Carbone — Kac–Moody groups and automorphic forms in low dimensional supergravity theories

Kathrin Bringmann, Karl Mahlburg and Antun Milas — The LusztigMacdonaldWall polynomial conjectures and $q$difference equations

Lisa Carbone and Frank Wagner — Uniqueness of representation–theoretic hyperbolic Kac–Moody groups over $\mathbb {Z}$

Jürgen Fuchs and Christoph Schweigert — Coends in conformal field theory

Haisheng Li — Remarks on $\phi $coordinated modules for quantum vertex algebras

André Henriques — The classification of chiral WZW models by $H^4_+(BG,\mathbb {Z})$

YiZhi Huang — Some open problems in mathematical twodimensional conformal field theory

Naihuan Jing, Chad R. Mangum and Kailash C. Misra — On realization of some twisted toroidal Lie algebras

James Lepowsky and Jinwei Yang — Twisted generating functions incorporating singular vectors in Verma modules and their localizations, I

Yusuke Arike, Kiyokazu Nagatomo and Yuichi Sakai — Characterization of the simple Virasoro vertex operator algebras with 2 and 3dimensional space of characters

David Radnell, Eric Schippers and Wolfgang Staubach — Quasiconformal Teichmüller theory as an analytical foundation for twodimensional conformal field theory

A. M. Semikhatov — Centralizing the centralizers

Nolan R. Wallach — On Neeman’s gradient flows


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This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana.
Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by YiZhi Huang summarizing some major open problems in these areas, in particular as they pertain to twodimensional conformal field theory.
Graduate students and research mathematicians interested in representation theory, vertex algebras, conformal field theory and related areas.

Articles

Darlayne Addabbo and Maarten Bergvelt — Generalizations of $Q$systems and orthogonal polynomials from representation theory

Dražen Adamović and Antun Milas — Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory

Ling Bao and Lisa Carbone — Kac–Moody groups and automorphic forms in low dimensional supergravity theories

Kathrin Bringmann, Karl Mahlburg and Antun Milas — The LusztigMacdonaldWall polynomial conjectures and $q$difference equations

Lisa Carbone and Frank Wagner — Uniqueness of representation–theoretic hyperbolic Kac–Moody groups over $\mathbb {Z}$

Jürgen Fuchs and Christoph Schweigert — Coends in conformal field theory

Haisheng Li — Remarks on $\phi $coordinated modules for quantum vertex algebras

André Henriques — The classification of chiral WZW models by $H^4_+(BG,\mathbb {Z})$

YiZhi Huang — Some open problems in mathematical twodimensional conformal field theory

Naihuan Jing, Chad R. Mangum and Kailash C. Misra — On realization of some twisted toroidal Lie algebras

James Lepowsky and Jinwei Yang — Twisted generating functions incorporating singular vectors in Verma modules and their localizations, I

Yusuke Arike, Kiyokazu Nagatomo and Yuichi Sakai — Characterization of the simple Virasoro vertex operator algebras with 2 and 3dimensional space of characters

David Radnell, Eric Schippers and Wolfgang Staubach — Quasiconformal Teichmüller theory as an analytical foundation for twodimensional conformal field theory

A. M. Semikhatov — Centralizing the centralizers

Nolan R. Wallach — On Neeman’s gradient flows