دانلود کتاب Lectures on Algebraic Categorification

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Preface......Page 5
Contents......Page 7
The idea of categorification......Page 11
Grothendieck group......Page 12
(Pre)categorification of an F-module......Page 14
Graded setup......Page 15
Some constructions......Page 16
Naïve categorification......Page 19
Weak categorification......Page 21
2-categories......Page 22
(Genuine) categorification......Page 24
2-representations of 2-categories......Page 27
Fiat-categories......Page 28
Principal 2-representations of fiat-categories......Page 29
Cells modules......Page 30
Naturally commuting functors......Page 32
Definition of category O......Page 35
Verma modules......Page 36
Block decomposition......Page 37
BGG reciprocity and quasi-hereditary structure......Page 38
Tilting modules and Ringel self-duality......Page 39
Parabolic category O......Page 40
gl_2-example......Page 41
Projective functors......Page 43
Translations through walls......Page 44
Description via Harish-Chandra bimodules......Page 45
Shuffling functors......Page 46
Singular braid monoid......Page 48
gl_2-example......Page 49
Twisting functors......Page 51
Completion functors......Page 53
Alternative description via (co)approximations......Page 55
Serre functor......Page 56
Double centralizer property......Page 57
Grading on B_......Page 58
Hecke algebra......Page 60
Categorification of the right regular H-module......Page 61
Combinatorics of O_lambda......Page 62
Soergel bimodules......Page 65
Kazhdan–Lusztig cells......Page 66
Cell modules......Page 67
Categorification of the induced sign module......Page 68
Categorification of Specht modules......Page 69
Categorification of cell modules......Page 71
Categorification of permutation modules......Page 72
Parabolic analogues of O......Page 74
Categorification of induced cell modules......Page 75
Quadratic dual of a positively graded algebra......Page 77
Linear complexes of projectives......Page 78
Koszul duality......Page 80
Alternative categorification of the permutation module......Page 82
The algebra U_v(sl_2)......Page 85
Finite dimensional representations of U_v(sl_2)......Page 86
Categorification of V_1^otimes n......Page 87
Categorification of V_n......Page 89
Koszul dual picture......Page 90
Kauffman bracket and Jones polynomial......Page 91
Quantum sl_2-link invariants......Page 92
Functorial quantum sl_2-link invariants......Page 94
Genuine sl_2-categorification......Page 97
Affine Hecke algebras......Page 98
Morphisms of sl_2-categorifications......Page 99
Minimal sl_2-categorification of simple finite-dimensional modules......Page 100
sl_2-categorification on category O......Page 101
Categorification of the simple reflection......Page 102
Jucys–Murphy elements and formal characters......Page 103
Induction and restriction......Page 104
Broué's conjecture......Page 105
Broué's conjecture for S_n......Page 106
Divided powers......Page 107
Wedderburn basis for C[S_n]......Page 109
Kostant's problem......Page 110
Structure of induced modules......Page 112
Exercises......Page 115
Bibliography......Page 119
Index......Page 127