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Softcover ISBN:  9780821827161 
Product Code:  CONM/297 
List Price:  $130.00 
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Product Code:  CONM/297.E 
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Softcover ISBN:  9780821827161 
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Book DetailsContemporary MathematicsVolume: 297; 2002; 334 ppMSC: Primary 17; Secondary 81; 82
Because of its many applications to mathematics and mathematical physics, the representation theory of infinitedimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, “InfiniteDimensional 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.
ReadershipGraduate students and research mathematicians interested in infinitedimensional Lie algebras and its applications in mathematical physics.

Table of Contents

Articles

Stephen Berman, Yuly Billig and Jacek Szmigielski — Vertex operator algebras and the representation theory of toroidal algebras [ MR 1919810 ]

Vyjayanthi Chari and Michael Kleber — Symmetric functions and representations of quantum affine algebras [ MR 1919811 ]

Ben L. Cox — Two realizations of toroidal $\mathfrak {sl}_2(\Bbb C)$ [ MR 1919812 ]

Chongying Dong, Haisheng Li and Geoffrey Mason — Vertex Lie algebras, vertex Poisson algebras and vertex algebras [ MR 1919813 ]

Alex J. Feingold and Michael D. Weiner — Type A fusion rules from elementary group theory [ MR 1919814 ]

Jürgen Fuchs and Christoph Schweigert — Lie algebra automorphisms in conformal field theory [ MR 1919815 ]

Yuji Hara, Michio Jimbo, Hitoshi Konno, Satoru Odake and Jun’ichi Shiraishi — On LepowskyWilson’s $\scr Z$algebra [ MR 1919816 ]

G. Hatayama, A. Kuniba, M. Okado, T. Takagi and Y. Yamada — Scattering rules in soliton cellular automata associated with crystal bases [ MR 1919817 ]

Barry M. McCoy — Algebra versus analysis in statistical mechanics and quantum field theory [ MR 1919818 ]

Antun Milas — Weak modules and logarithmic intertwining operators for vertex operator algebras [ MR 1919819 ]

Anne Schilling and S. Ole Warnaar — Conjugate Bailey pairs: from configuration sums and fractionallevel string functions to Bailey’s lemma [ MR 1919820 ]

Monica Vazirani — Irreducibility of affine Hecke algebra modules induced from Specht modules [ MR 1919821 ]

Weiqiang Wang — Algebraic structures behind Hilbert schemes and wreath products [ MR 1919822 ]

Wenhua Zhao — Some generalizations of genus zero twodimensional conformal field theory [ MR 1919823 ]


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Because of its many applications to mathematics and mathematical physics, the representation theory of infinitedimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, “InfiniteDimensional 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 infinitedimensional Lie algebras and its applications in mathematical physics.

Articles

Stephen Berman, Yuly Billig and Jacek Szmigielski — Vertex operator algebras and the representation theory of toroidal algebras [ MR 1919810 ]

Vyjayanthi Chari and Michael Kleber — Symmetric functions and representations of quantum affine algebras [ MR 1919811 ]

Ben L. Cox — Two realizations of toroidal $\mathfrak {sl}_2(\Bbb C)$ [ MR 1919812 ]

Chongying Dong, Haisheng Li and Geoffrey Mason — Vertex Lie algebras, vertex Poisson algebras and vertex algebras [ MR 1919813 ]

Alex J. Feingold and Michael D. Weiner — Type A fusion rules from elementary group theory [ MR 1919814 ]

Jürgen Fuchs and Christoph Schweigert — Lie algebra automorphisms in conformal field theory [ MR 1919815 ]

Yuji Hara, Michio Jimbo, Hitoshi Konno, Satoru Odake and Jun’ichi Shiraishi — On LepowskyWilson’s $\scr Z$algebra [ MR 1919816 ]

G. Hatayama, A. Kuniba, M. Okado, T. Takagi and Y. Yamada — Scattering rules in soliton cellular automata associated with crystal bases [ MR 1919817 ]

Barry M. McCoy — Algebra versus analysis in statistical mechanics and quantum field theory [ MR 1919818 ]

Antun Milas — Weak modules and logarithmic intertwining operators for vertex operator algebras [ MR 1919819 ]

Anne Schilling and S. Ole Warnaar — Conjugate Bailey pairs: from configuration sums and fractionallevel string functions to Bailey’s lemma [ MR 1919820 ]

Monica Vazirani — Irreducibility of affine Hecke algebra modules induced from Specht modules [ MR 1919821 ]

Weiqiang Wang — Algebraic structures behind Hilbert schemes and wreath products [ MR 1919822 ]

Wenhua Zhao — Some generalizations of genus zero twodimensional conformal field theory [ MR 1919823 ]