Ebook: Symmetries, Integrable Systems and Representations

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011.

Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.

Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

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This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Universit? Claude Bernard Lyon 1, France in December 13th to 16th, 2011.

Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.

Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

---

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Universit? Claude Bernard Lyon 1, France in December 13th to 16th, 2011.

Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.

Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Content:
Front Matter....Pages I-X
Generating Series of the Poincar? Polynomials of Quasihomogeneous Hilbert Schemes....Pages 1-13
Slavnov Determinants, Yang–Mills Structure Constants, and Discrete KP....Pages 15-33
Monodromy of Partial KZ Functors for Rational Cherednik Algebras....Pages 35-63
Category of Finite Dimensional Modules over an Orthosymplectic Lie Superalgebra: Small Rank Examples....Pages 65-84
A Classification of Roots of Symmetric Kac-Moody Root Systems and Its Application....Pages 85-132
Fermions Acting on Quasi-local Operators in the XXZ Model....Pages 133-154
The Romance of the Ising Model....Pages 155-173
A ?3-Orbifold Theory of Lattice Vertex Operator Algebra and ?3-Orbifold Constructions....Pages 175-193
Words, Automata and Lie Theory for Tilings....Pages 195-241
Toward Berenstein-Zelevinsky Data in Affine Type A, Part III: Proof of the Connectedness....Pages 243-261
Quiver Varieties and Tensor Products, II....Pages 263-295
Derivatives of Schur, Tau and Sigma Functions on Abel-Jacobi Images....Pages 297-318
Pad? Interpolation for Elliptic Painlev? Equation....Pages 319-344
Non-commutative Harmonic Oscillators....Pages 345-359
The Inversion Formula of Polylogarithms and the Riemann-Hilbert Problem....Pages 361-402
Some Remarks on the Quantum Hall Effect....Pages 403-428
Ordinary Differential Equations on Rational Elliptic Surfaces....Pages 429-462
On the Spectral Gap of the Kac Walk and Other Binary Collision Processes on d-Dimensional Lattice....Pages 463-482
A Restricted Sum Formula for a q-Analogue of Multiple Zeta Values....Pages 483-490
A Trinity of the Borcherds ?-Function....Pages 491-496
Sum Rule for the Eight-Vertex Model on Its Combinatorial Line....Pages 497-513
....Pages 515-541