Representations of Lie Algebras, Quantum Groups and Related Topics

Cover......Page 1
Title page......Page 2
Contents......Page 4
Preface......Page 6
1. Introduction......Page 8
2. The CKP hierarchy and its two bosonizations: overview......Page 11
3. Graded dimensions and character identities......Page 22
4. Appendix......Page 39
References......Page 40
1. Introduction......Page 42
2. Invariants......Page 43
3. Classification up to dimension 7......Page 45
4. Oscillator Lie superalgebras......Page 49
References......Page 51
1. Introduction......Page 54
2. Quantum affine algebra ��_{��}(̂����(2))......Page 55
3. Ω-operators and the Kashiwara algebra ��_{��}......Page 57
4. Quantized imaginary Verma modules and category ��^{��}_{��ℯ��,����}......Page 59
5. Imaginary crystal lattice and imaginary crystal basis......Page 62
References......Page 65
On the module structure of the center of hyperelliptic Krichever-Novikov algebras......Page 68
1. Introduction......Page 102
2. Classification of nilpotent Leibniz algebras with dim(��²)=3 and dim(��������(��))=1......Page 104
3. Classification of 5-dimensional complex nilpotent Leibniz algebras......Page 108
References......Page 125
1. Introduction......Page 128
2. Gelfand-Tsetlin modules for ����(��)......Page 129
3. Gelfand-Tsetlin modules with tableaux realization for ����(��)......Page 131
4. Irreducible Gelfand-Tsetlin modules in the principal block......Page 134
5. ��₂₁-localization of Gelfand-Tsetlin modules in the principal block......Page 138
References......Page 139
1. Kac-Moody algebras of affine types......Page 142
2. Fusion rings associated to Kac-Moody algebras of affine types......Page 143
3. Twining formula and Verlinde formula......Page 145
4. Proofs......Page 148
5. Modular S-matrix......Page 152
References......Page 153
1. Introduction......Page 156
2. Generalized quantum groups......Page 157
3. Kostant-Lusztig \bA-form......Page 165
References......Page 170
1. Introduction......Page 172
2. Catalan expansion of binomial coefficients......Page 174
3. Alternating Jacobsthal triangle......Page 181
4. ��-deformation......Page 186
5. ��-analogue of ��-deformation......Page 189
References......Page 192
1. Introduction......Page 194
2. Notation and preliminaries......Page 195
3. Hecke algebras and walk algebras......Page 198
4. Change of basis formula......Page 200
5. Counting points in Kac-Moody flag varieties......Page 202
6. Some connections to other work......Page 205
References......Page 209
1. Introduction......Page 212
2. Kac-Moody algebra of type ��_{2��}⁽¹⁾......Page 215
3. Kac-Moody algebra of type ��_{2��}⁽²⁾......Page 217
4. mKdV equations......Page 219
5. Tangent maps to Miura maps......Page 223
6. Critical points of master functions and generation of tuples of polynomials......Page 226
7. Critical points of master functions and Miura opers......Page 231
8. Vector fields......Page 236
References......Page 239
Back Cover......Page 242