Symmetries, Integrable Systems and Representations

✍ Scribed by N. Arbesfeld, O. Schiffmann (auth.), Kenji Iohara, Sophie Morier-Genoud, Bertrand Rémy (eds.)

• Publisher: Springer-Verlag London
• Year: 2013
• Tongue: English
• Leaves: 632
• Series: Springer Proceedings in Mathematics & Statistics 40
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-X
A Presentation of the Deformed W 1+∞ Algebra....Pages 1-13
Generating Series of the Poincaré Polynomials of Quasihomogeneous Hilbert Schemes....Pages 15-33
PBW-filtration over ℤ and Compatible Bases for V ℤ ( λ ) in Type A n and C n ....Pages 35-63
On the Subgeneric Restricted Blocks of Affine Category $\mathcal{O}$ at the Critical Level....Pages 65-84
Slavnov Determinants, Yang–Mills Structure Constants, and Discrete KP....Pages 85-132
Monodromy of Partial KZ Functors for Rational Cherednik Algebras....Pages 133-154
Category of Finite Dimensional Modules over an Orthosymplectic Lie Superalgebra: Small Rank Examples....Pages 155-173
Monoidal Categorifications of Cluster Algebras of Type A and D ....Pages 175-193
A Classification of Roots of Symmetric Kac-Moody Root Systems and Its Application....Pages 195-241
Fermions Acting on Quasi-local Operators in the XXZ Model....Pages 243-261
The Romance of the Ising Model....Pages 263-295
$A^{(1)}_{n}$ -Geometric Crystal Corresponding to Dynkin Index i =2 and Its Ultra-Discretization....Pages 297-318
A ℤ 3 -Orbifold Theory of Lattice Vertex Operator Algebra and ℤ 3 -Orbifold Constructions....Pages 319-344
Words, Automata and Lie Theory for Tilings....Pages 345-359
Toward Berenstein-Zelevinsky Data in Affine Type A , Part III: Proof of the Connectedness....Pages 361-402
Quiver Varieties and Tensor Products, II....Pages 403-428
Derivatives of Schur, Tau and Sigma Functions on Abel-Jacobi Images....Pages 429-462
Padé Interpolation for Elliptic Painlevé Equation....Pages 463-482
Non-commutative Harmonic Oscillators....Pages 483-490
The Inversion Formula of Polylogarithms and the Riemann-Hilbert Problem....Pages 491-496
Some Remarks on the Quantum Hall Effect....Pages 497-513
Ordinary Differential Equations on Rational Elliptic Surfaces....Pages 515-541
On the Spectral Gap of the Kac Walk and Other Binary Collision Processes on d -Dimensional Lattice....Pages 543-560
A Restricted Sum Formula for a q -Analogue of Multiple Zeta Values....Pages 561-573
A Trinity of the Borcherds Φ -Function....Pages 575-597
Sum Rule for the Eight-Vertex Model on Its Combinatorial Line....Pages 599-637

✦ Subjects

Associative Rings and Algebras;Special Functions;Combinatorics;Mathematical Physics;Mathematical Methods in Physics;Quantum Field Theories, String Theory