Physics And Combinatorics, Procs Of Nagoya 1999 Intl WkshpAnatol N Kirillov, Akihiro Tsuchiya, Hiroshi Umemura This volume contains research and review papers on different branches of mathematics and mathematical physics, written by the leading specialists. Among the contributed papers are articles on: (i) multiple basic hypergeometric functions with applications to the number theory, (ii) birational representations of affine Weyl groups with applications to discrete integrable systems, (iii) algebraic geometry and Painleve VI, and (iv) combinatorics of Kostka-Foulkes polynomials. |
Contents
| 1 | |
| 11 | |
| 16 | |
Origin of Exclusion Statistics Haldane Liquids SutherlandWu Equations Grand Partition Function and LeeYang Theorem ... | 30 |
Symmetric Spaces over Finite Fields FrobeniusSchur Indices and Symmetric Function Identities ... | 70 |
Ubiquity of Kostka Polynomials | 85 |
Transformations of Un + 1 Multiple Basic Hypergeometric Series | 201 |
Kashaevs Invariant and the Volume of a Hyperbolic Knot after Y Yokota | 244 |
Integral Solutions of Hypergeometric gDifference Systems with q 1 | 273 |
Birational Weyl Group Action Arising from a Nilpotent Poisson Algebra | 287 |
Painleve Equations and Deformations of Rational Surfaces with Rational Double Points | 320 |
Representation of Umemura Polynomials for the Sixth Painleve Equation by the Generalized Jacobi Polynomials ... | 366 |
Two Relations that Generalize the gSerre Relations and the DolanGrady Relations | 377 |
Common terms and phrases
605 summation affine automorphism Bailey Transform basic hypergeometric series birational C₁ combinatorial configurations conjecture Corollary corresponding curve decomposition define definition denote dimensional duality Ehrhart polynomial eigenvalue equal example exclusion statistics fermionic fermionic formula finite grand partition function Hall-Littlewood Hence identity integer irreducible isomorphic Kirillov Kostant partition function Kostka polynomials Kostka-Foulkes polynomials lattice Lemma Leonard pair Lett Lie algebra linear Math matrix morphism multiple notation obtain Painlevé equations parabolic Kostka polynomials parameter Phys Poisson algebra polytope positive integer proof Proposition q-analog quantum rectangular shape partitions relations representation S. C. Milne satisfy Schur functions Section sequence of rectangular Show singularity summation theorem symmetric functions TD pair tetrahedron theory Tridiagonal very-well-poised W₁ weight Weyl group X[to Young tableaux Z[to αβ