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This volume is the proceedings of the conference 'Algebraic Analysis and Around', in honor of Professor Masaki Kashiwara's 60th birthday. The conference was held in Kyoto in June 2007. Most of the papers are based on talks given at the conference, and the subjects discussed include D-modules, micro-local analysis, representation theory, integrable systems, to which Kashiwara's contribution and influence are really profound. The readers may find groundbreaking materials for the future in mathematics.

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.

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.