Ebook: Physical Combinatorics
- Tags: Combinatorics, Theoretical Mathematical and Computational Physics
- Series: Progress in Mathematics 191
- Year: 2000
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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
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
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
Content:
Front Matter....Pages i-ix
An Insertion Scheme for C n Crystals....Pages 1-48
On the Combinatorics of Forrester-Baxter Models....Pages 49-103
Combinatorial R Matrices for a Family of Crystals: C n (1) and A 2n-1 (2) Cases....Pages 105-139
Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators....Pages 141-162
A Generalization of the q-Saalsch?tz Sum and the Burge Transform....Pages 163-183
The Bethe Equation at q = 0, the M?bius Inversion Formula, and Weight Multiplicities I: The sl (2) Case....Pages 185-216
Hidden E-Type Structures in Dilute A Models....Pages 217-247
Canonical Bases of Higher-Level q-Deformed Fock Spaces and Kazhdan-Lusztig Polynomials....Pages 249-299
Finite-Gap Difference Operators with Elliptic Coefficients and Their Spectral Curves....Pages 301-317
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
Content:
Front Matter....Pages i-ix
An Insertion Scheme for C n Crystals....Pages 1-48
On the Combinatorics of Forrester-Baxter Models....Pages 49-103
Combinatorial R Matrices for a Family of Crystals: C n (1) and A 2n-1 (2) Cases....Pages 105-139
Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators....Pages 141-162
A Generalization of the q-Saalsch?tz Sum and the Burge Transform....Pages 163-183
The Bethe Equation at q = 0, the M?bius Inversion Formula, and Weight Multiplicities I: The sl (2) Case....Pages 185-216
Hidden E-Type Structures in Dilute A Models....Pages 217-247
Canonical Bases of Higher-Level q-Deformed Fock Spaces and Kazhdan-Lusztig Polynomials....Pages 249-299
Finite-Gap Difference Operators with Elliptic Coefficients and Their Spectral Curves....Pages 301-317
....