Physics and Combinatorics 2000: Proceedings of the Nagoya 2000 International Workshop : Graduate School of Mathematics, Nagoya University, 21-26 August, 2000Anatol N. Kirillov, Nadejda Liskova 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 Twists in Quantum Teichmller Theory (R Kashaev); Introduction to Tropical Combinatorics (A Kirillov); Transition on Grothendieck Polynomials (A Lascoux); Generalized HAlder''s Theorem for Multiple Gamma Function (M Nishizawa); Quantum Calogero-Moser Models: Complete Integrability for All the Root Systems (R Sasaki); Simplification of Thermodynamic BetheOCoAnsatz Equations (M Takahashi); and other papers. Readership: Researchers and graduates in mathematical physics and combinatorics & graph theory." |
Contents
Preface | 1 |
Exclusion Statistics and Chiral Partition Function | 22 |
Forresters Constant Term Conjecture and its qanalogue | 49 |
On the Spectrum of Dehn Twists in Quantum Teichmüller Theory | 63 |
Introduction to Tropical Combinatorics | 82 |
Bethes States for Generalized XXX and XXZ models | 151 |
Transition on Grothendieck Polynomials | 164 |
Tableau Representation for Macdonalds Ninth Variation of | 180 |
Tanalogue of the qcharacters of Finite Dimensional | 196 |
Generalized Hölders Theorem for Multiple Gamma Function | 220 |
Complete Integrability | 233 |
Green Functions Associated to Complex Reflection Groups | 281 |
Simplification of Thermodynamic BetheAnsatz Equations | 299 |
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Common terms and phrases
action affine symmetric group An² bijection birational Calogero Calogero-Moser models character cocharge coefficients combinatorial compute conjecture conserved quantities Corollary Coxeter group decomposition definition Dehn twist denote diagonal eigenfunctions equation explicit formula gamma function Gelfand-Tsetlin given Green functions Grothendieck polynomials GT-patterns Hamiltonian Hilbert scheme homomorphism integer inverse involution isomorphism Kirillov Lascoux Laurent's polynomial Lax pair Lemma Lett Lie algebra Lusztig Macdonald polynomials Math matrix minor determinant monomial multiple gamma function N₁ obtain operators permutation Phys piece-wise linear potential proof Proposition rational recursion relation restricted partition function result Robinson-Schensted-Knuth correspondence root systems satisfy Schubert Schubert polynomials Schur functions Schützenberger Section semistandard Young tableaux space of triangles statistics symmetric functions symmetric group Teichmüller theory Theorem theory transformations triangles Xn Tropical image tropical version unipotent variables vector Weyl group Young tableaux ΡΕΔ