Quantum Groups The Loop Grassmannian And The Resolution

Main players.......Page 1
Relation to results by Kazhdan-Lusztig and Kashiwara-Tanisaki.......Page 2
The functor Q:......Page 4
The functor P:......Page 5
Relation to affine Hecke algebras.......Page 6
Organization of the paper.......Page 7
BookmarkTitle:......Page 8
A-forms of Uq.......Page 9
Frobenius functor.......Page 10
Ind- and pro-objects.......Page 12
Hopf-adjoint action.......Page 13
Cohomology of Hopf algebras.......Page 16
Reminder on dg-algebras and dg-modules.......Page 17
From coherent sheaves on N"0365N to [n]-modules.......Page 18
The principal block of U-modules.......Page 19
Induction.......Page 20
Quantum group Formality theorem.......Page 21
Digression: Deformation formality.......Page 22
Equivariance and finiteness conditions.......Page 23
Comparison of derived categories.......Page 25
Intertwining functors.......Page 27
Beginning of the proof of Theorem 3.5.5.......Page 28
A direct limit construction.......Page 29
Constructing an equivariant dg-resolution.......Page 31
DG-resolution of b.......Page 33
Main result.......Page 34
Comparison of functors.......Page 35
`Deformation' morphism.......Page 37
Proof of Theorem 5.4.5.......Page 38
The loop group.......Page 39
Geometric Satake equivalence.......Page 40
Fiber functors.......Page 41
Equivariant and Brylinski's filtrations.......Page 42
The regular perverse sheaf R.......Page 43
Main result.......Page 44
Some general results.......Page 45
Proof of Theorem 7.3.1:......Page 46
Equivariant version.......Page 47
A fiber functor on perverse sheaves.......Page 48
BookmarkTitle:......Page 49
The affine flag manifold.......Page 50
An Ext-composition.......Page 51
Homogeneous coordinate ring of N"0365N as an Ext-algebra.......Page 52
Brylinski filtration in terms of Springer resolution (after Br).......Page 53
Proof of Theorem 8.5.2.......Page 54
Monodromic sheaves and extended affine flag manifold.......Page 56
Mixed categories.......Page 58
Mixed perverse sheaves.......Page 60
An Ext-formality result.......Page 62
Construction of the functors P and P'.......Page 64
Properties of the functor P'.......Page 65
Proof of Theorems 9.1.4 and 9.4.3.......Page 69
Equivalence of abelian categories.......Page 70
Equivariant coherent sheaves on N.......Page 72
Induction.......Page 73
Quantum group cohomology via the loop Grassmannian.......Page 74
BookmarkTitle:......Page 75
Proof of Theorem 10.2.3.......Page 76