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Recent Developments in Infinite-dimensional Lie Algebras and Conformal Field Theory

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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.
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Table of Contents

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

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