دانلود کتاب Quantum groups and quantum cohomology

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Chapter 1. Introduction
1.1. Fundamental structures and conjectures
1.2. Baxter subalgebras and quantum multiplication
1.3. Quantum multiplication by divisors
1.4. Shift operators and qKZ
1.5. Yangian of gl(1)\"0362gl(1) and instanton moduli
1.6. Further directions
1.7. Update
1.8. Acknowledgments
Part I. General Theory
Chapter 2. Nakajima varieties
2.1. Definition
2.2. Basic properties
2.3. Torus-fixed points
2.4. Tensor product of Nakajima varieties
2.5. Slices
2.6. Minuscule coweights
Chapter 3. Stable envelopes
3.1. Assumptions and conventions
3.2. Basic constructions
3.3. Characterization of stable envelopes
3.4. Lagrangian residues
3.5. Proof of existence
3.6. Torus restriction
3.7. Symplectic resolutions
Chapter 4. Properties of R-matrices
4.1. Definition and braid relations
4.2. Changing the torus
4.3. Covers and factorization of R-matrices
4.4. Adjoint operators
4.5. Unitarity
4.6. Action of Steinberg correspondences
4.7. Vacuum matrix elements
4.8. Classical R-matrices
4.9. Diagonal matrix elements of R-matrices
4.10. Flops and stable envelopes
Chapter 5. Yangians
5.1. Tensor products
5.2. Construction of Yangians
5.3. The Lie algebra gQ
5.4. Operators of classical multiplication
5.5. The structure of the Yangian
Chapter 6. Further properties of the Yangian
6.1. The core Yangian
6.2. Slices and intertwiners
6.3. The dual Yangian
6.4. Intertwiners and relations
6.5. Baxter subalgebras and Casimir connection
Chapter 7. Quantum multiplication
7.1. Preliminaries
7.2. Modified reduced operators
7.3. Broken curves
7.4. Proof of Theorem 7.2.1
7.5. Additivity
Chapter 8. Shift operators
8.1. Definition
8.2. Intertwining property
8.3. Shift operators are quantum operators
Chapter 9. Minuscule shifts and R-matrices
9.1. Setup
9.2. Properness
9.3. Computation of S()
Chapter 10. Quantum multiplication by divisors
10.1. Classical multiplication by divisors
10.2. Quantum operators
Chapter 11. Cotangent bundles of Grassmannians
11.1. Quantum cohomology
11.2. The stable basis
11.3. Yangian action
Part II. Instanton moduli
Chapter 12. Classical r-matrix and gl(1)\"0362gl(1).
12.1. Setup
12.2. Baranovsky operators
12.3. Proof of Theorem 12.2.1
12.4. Classical r-matrix
Chapter 13. Free bosons
13.1. Fock spaces
13.2. Insertions and coproducts
13.3. Virasoro algebra
13.4. Reflection operator
Chapter 14. The full R-matrix
14.1. Zero modes
14.2. Cup product by divisor
14.3. R-matrix as a Virasoro intertwiner
14.4. The 1/u expansion of R
Chapter 15. Quantum multiplication for M(r,n)
15.1. Explicit formulas
15.2. Generation statement
Chapter 16. Gamma functions
16.1. The bundle V\"0362V
16.2. Barnes\' -function
16.3. The matrix R\"0362R
Chapter 17. Core Yangian modulo
17.1. Semiclassical R-matrix
17.2. Stable basis for `39`42`\"613A``45`47`\"603AHilbn
17.3. Differential operators on C and gl()
17.4. Plücker relations
Chapter 18. The Yangian of gl(1)\"0362gl(1)
18.1. Generators of the core Yangian
18.2. Slices and screening operators
Chapter 19. Yangian and vertex algebras
19.1. The operator Q\"055BQcl
19.2. Yangian and W-algebras
Bibliography