Physical Combinatorics

ISBN-13: 9780817641757 / Angielski / Twarda / 2000 / 317 str.

Masaki Kashiwara; Tetsuji Miwa; M. Kashiwara

Opis

This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. 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 of Hamiltonians. this text presents results and ideas from three viewpoints: representation theory; integrable models; and combinatorics.

Spis treści

Preface.-An Insertion Scheme for Cn Crystals.-On the Combinatorics of Forrester Baxter Models.-Combinatorial R Matrices for a Family of Crystals: Cn(1) and A 2n-1(2) Cases.-Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators.-A Generalization of the q-Saalschütz Sum and the Burge Transform.-The Bethe Equation at q=0, the Möbius Inversion Formula, and Weight Multiplicities I: The sl(2) Case.-Hidden E-Type Structures in Dilute A Models.-Canonical Basses of High-Level q-Deformed Fock Spaces and Kazhdan Lusztig Polynomials.-Finite-Gap Difference Operators with Elliptic Coefficients and Their Spectral Curves.