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Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory
Edited by: Stephen Berman, University of Saskatchewan, Saskatoon, SK, Canada, Paul Fendley, University of Virginia, Charlottesville, VA, Yi-Zhi Huang, Rutgers University, Piscataway, NJ, Kailash Misra, North Carolina State University, Raleigh, NC, and Brian Parshall, University of Virginia, Charlottesville, VA
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Contemporary Mathematics
2002; 334 pp; softcover
Volume: 297
ISBN-10: 0-8218-2716-2
ISBN-13: 978-0-8218-2716-1
List Price: US$91 Member Price: US$72.80
Order Code: CONM/297

Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, "Infinite-Dimensional Lie Theory and Conformal Field Theory", held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field.

This conference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlighted applications to conformal field theory, integrable and disordered systems.

Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.

Graduate students and research mathematicians interested in infinite-dimensional Lie algebras and its applications in mathematical physics.

• S. Berman, Y. Billig, and J. Szmigielski -- Vertex operator algebras and the representation theory of toroidal algebras
• V. Chari and M. Kleber -- Symmetric functions and representations of quantum affine algebras
• B. L. Cox -- Two realizations of toroidal $$\mathfrak{sl}_2(\mathbb C)$$
• C. Dong, H. Li, and G. Mason -- Vertex Lie algebras, vertex Poisson algebras and vertex algebras
• A. J. Feingold and M. D. Weiner -- Type A fusion rules from elementary group theory
• J. Fuchs and C. Schweigert -- Lie algebra automorphisms in conformal field theory
• Y. Hara, M. Jimbo, H. Konno, S. Odake, and J. Shiraishi -- On Lepowsky-Wilson's $$\mathcal{Z}$$-algebra
• G. Hatayama, A. Kuniba, M. Okado, T. Takagi, and Y. Yamada -- Scattering rules in soliton cellular automata associated with crystal bases
• B. M. McCoy -- Algebra versus analysis in statistical mechanics and quantum field theory
• A. Milas -- Weak modules and logarithmic intertwining operators for vertex operator algebras
• A. Schilling and S. O. Warnaar -- Conjugate Bailey pairs
• M. Vazirani -- Irreducibility of affine Hecke algebra modules induced from Specht modules
• W. Wang -- Algebraic structures behind Hilbert schemes and wreath products
• W. Zhao -- Some generalizations of genus zero two-dimensional conformal field theory