Physical Combinatorics (progress In Mathematics)

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 Edited By Masaki Kashiwara, Tetsuji Miwa. 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 -Saalschütz Sum and the Burge Transform....Pages 163-183 The Bethe Equation at q = 0, the Möbius 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 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 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. "Taking into account the various criss-crossing among mathematical subjects, 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 above-mentioned fields."--Jacket