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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
Brian Parshall University of Virginia, Charlottesville, VA
Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory
Softcover ISBN:  978-0-8218-2716-1
Product Code:  CONM/297
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7887-3
Product Code:  CONM/297.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-2716-1
eBook: ISBN:  978-0-8218-7887-3
Product Code:  CONM/297.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory
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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
Brian Parshall University of Virginia, Charlottesville, VA
Softcover ISBN:  978-0-8218-2716-1
Product Code:  CONM/297
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7887-3
Product Code:  CONM/297.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-2716-1
eBook ISBN:  978-0-8218-7887-3
Product Code:  CONM/297.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2972002; 334 pp
    MSC: Primary 17; Secondary 81; 82;

    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.

    Readership

    Graduate students and research mathematicians interested in infinite-dimensional 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 Lepowsky-Wilson’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 fractional-level 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 two-dimensional conformal field theory [ MR 1919823 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2972002; 334 pp
MSC: Primary 17; Secondary 81; 82;

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.

Readership

Graduate students and research mathematicians interested in infinite-dimensional 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 Lepowsky-Wilson’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 fractional-level 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 two-dimensional conformal field theory [ MR 1919823 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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