Physics and Combinatorics, Procs of the Nagoya 2000 Intl Workshop

Preface......Page 6
CONTENTS......Page 8
1 Introduction......Page 10
2 The Bridgeland-King-Reid theorem......Page 14
3 Prior results on Hilbert schemes and polygraphs......Page 17
4 Main results......Page 19
5 Application to character formulas......Page 24
References......Page 29
1 Introduction......Page 31
2 Ideal g-on Gas and Recursion Relation......Page 32
3 Generalization: Yangian Symmetry......Page 41
4 Concluding Remarks......Page 49
References......Page 55
1 Introduction......Page 58
2 Forrester's conjecture......Page 59
3 q-analogue......Page 64
References......Page 71
1 Introduction......Page 72
2 Quantum dilogarithm......Page 73
3 The basic algebraic system......Page 75
4 The mapping class group representation......Page 77
5 Diagonalizing the Dehn twist......Page 81
6 Braiding and R-matrix......Page 83
7 Conclusion......Page 87
References......Page 89
Introduction to Tropical Combinatorics......Page 91
1 Introduction......Page 92
2 Basic Definitions......Page 99
3 Explicit formulae: piece-wise linear version......Page 121
4 Explicit formulae: tropification......Page 124
References......Page 157
1 Introduction......Page 160
2 Rogers-Ramanujan's type identity......Page 161
3 XXZ -> XXX bijection......Page 167
References......Page 172
1 Introduction......Page 173
2 0-Hecke algebra......Page 175
4 Stable part by restriction or symmetrization.......Page 178
5 Transition on Grothendieck polynomials......Page 181
6 Variations among determinantal expressions......Page 185
References......Page 187
Introduction......Page 189
1 Weyl formula and Jacobi-Trudi formula......Page 190
2 Tableau representation......Page 195
3 Specifying the tableau variables......Page 200
References......Page 204
1 The quantum loop algebra......Page 205
2 Standard modules......Page 208
3 t-analogues of q-characters......Page 210
4 Step 3......Page 211
5 Step 1......Page 212
6 Step 2......Page 215
7 Restriction to Uc(g)......Page 218
8 Quiver varieties......Page 220
References......Page 227
1 Introduction......Page 229
2 Barnes' Multiple Gamma Function......Page 230
3 Generalized Holder's Theorem......Page 232
4 Differential Relation in a Special Case......Page 238
References......Page 240
1 Introduction......Page 242
2 Quantum Calogero-Moser Models......Page 247
3 Coxeter invariant excited states  triangularity and spectrum......Page 252
4 Quantum Lax pair and quantum conserved quantities......Page 262
5 Algebraic construction of excited states I......Page 267
6 l operators......Page 270
7 Algebraic construction of excited states II......Page 273
8 Universal proof of involution of quantum conserved quantities for type I II and III models......Page 278
9 Summary comments and outlook......Page 280
References......Page 285
0 Introduction......Page 290
1 A background from finite reductive groups......Page 292
2 Green functions associated to G(e 1 n)......Page 294
3 A combinatorial setting for G(e 1 n)......Page 296
References......Page 307
1 Introduction......Page 308
2 Derivation......Page 309
References......Page 313
1 Introduction......Page 314
2 A birational map R......Page 315
3 Combinatorial R-matrix......Page 320
4 Lusztig's bijection Ri'i......Page 322
5 Discrete Toda equation......Page 324
References......Page 326