Physics and Combinatorics : Proceedings of the Nagoya 2000 International Workshop, Nagoya University, 21-26 August 2000.

Physics and Combinatorics : Proceedings of the Nagoya 2000 International Workshop, Nagoya University, 21-26 August 2000.

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 possibl...

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Bibliographic Details
Main Author: Kirillov, Anatol N.
Other Authors: Liskova, Nadejda
Format: eBook
Language:English
Published: Singapore : World Scientific Publishing Company, 2001.
Subjects:
Combinatorial analysis > Congresses.
Mathematical physics > Congresses.
Combinatorial analysis
Mathematical physics
Conference papers and proceedings
Online Access:Click for online access
Table of 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

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