preface
chapter 0. introduction
chapter 1. symplectic geometry
1.1. symplectic manifolds
1.2. poisson algebras
1.3. poisson structures arising from noncommutative algebras
1.4. the moment map
1.5. coisotropic subvarieties
1.6. lagrangian families
chapter 2. mosaic
2.1. hilbert''s nullste!lensatz
2.2. atone algebraic varieties
2.3. the deformation construction
2.4. c*-actions on a projective variety
2.5. fixed point reduction
2.6. borel-moore homology
2.7. convolution in borel-moore homology
chapter 3. complex semisimple groups
3.1. semisimple lie algebras and flag varieties
3.2. nilpotent cone
3.3. the steinberg variety
3.4. lagrangian construction of the weyl group
3.5. geometric analysis of hz-action
3.6. irreducible representations of we~1 groups
3.7. applications of the jacobson-morozov theorem
chapter 4. springer theory for usln
4.1. geometric construction of the enveloping algebra
usinc
4.2. finite-dimensional simple slnc-modules
4.3. proof of the main theorem
4.4. stabilization
chapter 5. equivariant k-theory
5.1. equivariant resolutions
5.2. basic k-theoretic constructions
5.3. specialization in equivariant k-theory
5.4. the koszul complex and the thom isomorphism
5.5. cellular fibration lemma
5.6. the kinneth formula
5.7. projective bundle theorem and beilinson resolution
5.8. the chern character
5.9. the dimension filtration and "devissage"
5.10. the localization theorem
5.11. functoriality
chapter 6. flag varieties, k-theory, and harmonic polynomials
6.1. equivariant k-theory of the flag variety
6.2. equivariant k-theory of the steinberg variety
6.3. harmonic polynomials
6.4. w-harmonic polynomials and flag varieties
6.5. orbital varieties
6.6. the equivariant hilbert polynomial
6.7. kostant''s theorem on polynomial rings
chapter 7. hecke algebras and k-theory
7.1. affine weyl groups and hecke algebras
7.2. main theorems
7.3. case q = h deformation argument
7.4. hilbert polynomials and orbital varieties
7.5. the hecke algebra for sl2
7.6. pwof of the main theorem
chapter 8. representations of convolution algebras
8.1. standard modules
8.2. character formula for standard modules
8.3. constructible complexes
8.4. perverse sheaves and the classification theorem
8.5. the contravariant form
8.6. shed-theoretic analysis of the convolution algebra
8.7. projective modules over convolution algebra
8.8. a non-vanishing result
8.9. semi-small maps
bibliography
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