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Lie algebras, vertex operator algebras, and related topics. Conference in honor of J. Lepowsky and R. Wilson on the occasion ot their 70th birthdays, University of Notre Dame, Notre Dame, IN, USA, August 14–18, 2015. (English) Zbl 1373.17001

Contemporary Mathematics 695. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2666-8/pbk; 978-1-4704-4196-8/ebook). vi, 274 p. (2017).

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Publisher’s description: 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 Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
The articles of this volume will be reviewed individually.
Indexed articles:
Addabbo, Darlayne; Bergvelt, Maarten, Generalizations of \(Q\)-systems and orthogonal polynomials from representation theory, 1-13 [Zbl 1390.17041]
Adamović, Dražen; Milas, Antun, Some applications and constructions of intertwining operators in logarithmic conformal field theory, 15-27 [Zbl 1430.17080]
Bao, Ling; Carbone, Lisa, Kac-Moody groups and automorphic forms in low dimensional supergravity theories, 29-40 [Zbl 1431.20035]
Bringmann, Kathrin; Mahlburg, Karl; Milas, Antun, The Lusztig-Macdonald-Wall polynomial conjectures and \(q\)-difference equations. In honor of Jim Lepowsky and Robert Wilson, 41-49 [Zbl 1384.05014]
Carbone, Lisa; Wagner, Frank, Uniqueness of representation-theoretic hyperbolic Kac-Moody groups over \(\mathbb{Z}\), 51-64 [Zbl 1431.20036]
Fuchs, Jürgen; Schweigert, Christoph, Coends in conformal field theory, 65-81 [Zbl 1390.18004]
Li, Haisheng, Remarks on \(\phi\)-coordinated modules for quantum vertex algebras., 83-98 [Zbl 1430.17091]
Henriques, André, The classification of chiral WZW models by \(H^4_+(BG,\mathbb{Z})\), 99-121 [Zbl 1430.17086]
Huang, Yi-Zhi, Some open problems in mathematical two-dimensional conformal field theory, 123-138 [Zbl 1430.17087]
Jing, Naihuan; Mangum, Chad R.; Misra, Kailash C., On realization of some twisted toroidal Lie algebras, 139-148 [Zbl 1430.17077]
Lepowsky, James; Yang, Jinwei, Twisted generating functions incorporating singular vectors in Verma modules and their localizations, I, 149-173 [Zbl 1430.17025]
Arike, Yusuke; Nagatomo, Kiyokazu; Sakai, Yuichi, Characterization of the simple Virasoro vertex operator algebras with 2 and 3-dimensional space of characters, 175-204 [Zbl 1414.17017]
Radnell, David; Schippers, Eric; Staubach, Wolfgang, Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theory. Dedicated to Jim Lepowsky and Robert Wilson on the occasion of their 70th birthdays, 205-238 [Zbl 1393.30034]
Semikhatov, A. M., Centralizing the centralizers, 239-259 [Zbl 1386.16016]
Wallach, Nolan R., On Neeman’s gradient flows, 261-274 [Zbl 1388.14158]

MSC:

17-06 Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras
17B69 Vertex operators; vertex operator algebras and related structures
17B05 Structure theory for Lie algebras and superalgebras
17B45 Lie algebras of linear algebraic groups
81R15 Operator algebra methods applied to problems in quantum theory
81T05 Axiomatic quantum field theory; operator algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
00B25 Proceedings of conferences of miscellaneous specific interest
00B30 Festschriften

Biographic References:

Lepowsky, James; Wilson, Robert
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