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Physical Combinatorics

  • Textbook
  • © 2000

Overview

Editors:
  1. Masaki Kashiwara

    1. Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan

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  2. Tetsuji Miwa

    1. Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Mathematics (PM, volume 191)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. An Insertion Scheme for C n Crystals

    • T. H. Baker
    Pages 1-48

  3. On the Combinatorics of Forrester-Baxter Models

    • Omar Foda, Trevor A. Welsh
    Pages 49-103

  4. Combinatorial R Matrices for a Family of Crystals: C (1) n and A (2) 2n-1 Cases

    • Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi
    Pages 105-139

  5. Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators

    • Yasushi Komori
    Pages 141-162

  6. A Generalization of the q-Saalschütz Sum and the Burge Transform

    • Anne Schilling, S. Ole Warnaar
    Pages 163-183

  7. The Bethe Equation at q = 0, the Möbius Inversion Formula, and Weight Multiplicities I: The sl (2) Case

    • Atsuo Kuniba, Tomoki Nakanishi
    Pages 185-216

  8. Hidden E-Type Structures in Dilute A Models

    • J. Suzuki
    Pages 217-247

  9. Canonical Bases of Higher-Level q-Deformed Fock Spaces and Kazhdan-Lusztig Polynomials

    • Denis Uglov
    Pages 249-299

  10. Finite-Gap Difference Operators with Elliptic Coefficients and Their Spectral Curves

    • A. Zabrodin
    Pages 301-317
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Keywords

About this book

This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Recent developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics. For example, Young tableaux, which describe the basis of irreducible representations, appear in the Bethe Ansatz method in quantum spin chains as labels for the eigenstates for Hamiltonians.

Taking into account the various criss-crossing among mathematical subject, Physical Combinatorics presents new results and exciting ideas from three viewpoints; representation theory, integrable models, and combinatorics.

This volume will be of interest to mathematical physicists and graduate students in the the above-mentioned fields.

Contributors to the volume: T.H. Baker, O. Foda, G. Hatayama, Y. Komori, A. Kuniba, T. Nakanishi, M. Okado, A. Schilling, J. Suzuki, T. Takagi, D. Uglov, O. Warnaar, T.A. Welsh, A. Zabrodin

Editors and Affiliations

  • Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan

    Masaki Kashiwara, Tetsuji Miwa

Bibliographic Information

  • Book Title: Physical Combinatorics

  • Editors: Masaki Kashiwara, Tetsuji Miwa

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1378-9

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • Hardcover ISBN: 978-0-8176-4175-7Published: 16 June 2000

  • Softcover ISBN: 978-1-4612-7121-5Published: 15 October 2012

  • eBook ISBN: 978-1-4612-1378-9Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 317

  • Topics: Combinatorics, Theoretical, Mathematical and Computational Physics

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