Physics and combinatorics 2000 : proceedings of the Nagoya 2000 International Workshop : Graduate School of Mathematics, Nagoya University, 21-26 August, 2000 / editors, Anatol N. Kirillov, Nadejda Liskova.

Format:

Book

Conference/Event

Contributor:

Kirillov, Anatol N.

Liskova, Nadejda.

Conference Name:

International Workshop on Physics and Combinatorics (2nd : 2000 : Nagoya-shi, Japan)

International Workshop on Physics and Combinatorics

Language:

English

Subjects (All):

Combinatorial analysis--Congresses.

Combinatorial analysis.

Mathematical physics--Congresses.

Mathematical physics.

Physical Description:

1 online resource (329 p.)

Edition:

1st ed.

Other Title:

Proceedings of the Nagoya 2000 International Workshop, Physics and Combinatorics 2000

Place of Publication:

Singapore ; River Edge NJ : World Scientific, c2001.

Language Note:

English

Summary:

The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop. Contents: Vanishing Theorems and Character Formulas for the Hilbert Scheme of Points in the Plane (M Haiman); Exclusion Statistics and Chiral Partition Function (K Hikami); On the Spectrum of Dehn

Contents:

Preface; CONTENTS; Vanishing Theorems and Character Formulas for the Hilbert Scheme of Points in the Plane; 1 Introduction; 2 The Bridgeland-King-Reid theorem; 3 Prior results on Hilbert schemes and polygraphs; 4 Main results; 5 Application to character formulas; References; Exclusion Statistics and Chiral Partition Function; 1 Introduction; 2 Ideal g-on Gas and Recursion Relation; 3 Generalization: Yangian Symmetry; 4 Concluding Remarks; References; Forrester's Constant Term Conjecture and its q-analogue; 1 Introduction; 2 Forrester's conjecture; 3 q-analogue; References

On the Spectrum of Dehn Twists in Quantum Teichmuller Theory1 Introduction; 2 Quantum dilogarithm; 3 The basic algebraic system; 4 The mapping class group representation; 5 Diagonalizing the Dehn twist; 6 Braiding and R-matrix; 7 Conclusion; References; Introduction to Tropical Combinatorics; 1 Introduction; 2 Basic Definitions; 3 Explicit formulae: piece-wise linear version; 4 Explicit formulae: tropification; References; Bethe's States for Generalized XXX and XXZ models; 1 Introduction; 2 Rogers-Ramanujan's type identity; 3 XXZ -> XXX bijection; References

Transition on Grothendieck Polynomials1 Introduction; 2 0-Hecke algebra; 3 Symmetric Grothendieck Polynomials; 4 Stable part by restriction or symmetrization.; 5 Transition on Grothendieck polynomials; 6 Variations among determinantal expressions; References; Tableau Representation for Macdonald's Ninth Variation of Schur Functions; Introduction; 1 Weyl formula and Jacobi-Trudi formula; 2 Tableau representation; 3 Specifying the tableau variables; References; T-analogue of the q-characters of Finite Dimensional Representations of Quantum Affine Algebras; 1 The quantum loop algebra

2 Standard modules3 t-analogues of q-characters; 4 Step 3; 5 Step 1; 6 Step 2; 7 Restriction to Uc(g); 8 Quiver varieties; References; Generalized Holder's Theorem for Multiple Gamma Function; 1 Introduction; 2 Barnes' Multiple Gamma Function; 3 Generalized Holder's Theorem; 4 Differential Relation in a Special Case; References; Quantum Calogero-Moser Models: Complete Integrability for All the Root Systems; 1 Introduction; 2 Quantum Calogero-Moser Models; 3 Coxeter invariant excited states triangularity and spectrum; 4 Quantum Lax pair and quantum conserved quantities

5 Algebraic construction of excited states I6 l operators; 7 Algebraic construction of excited states II; 8 Universal proof of involution of quantum conserved quantities for type I II and III models; 9 Summary comments and outlook; References; Green Functions Associated to Complex Reflection Groups G(e 1 n); 0 Introduction; 1 A background from finite reductive groups; 2 Green functions associated to G(e 1 n); 3 A combinatorial setting for G(e 1 n); References; Simplification of Thermodynamic Bethe-Ansatz Equations; 1 Introduction; 2 Derivation; 3 Analytical solutions; References

A Birational Representation of Weyl Group Combinatorial R-matrix and Discrete Toda Equation

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611951542

9781281951540

1281951544

9789812810007

9812810005

OCLC:

879024829