Affine Hecke Algebras and Quantum Symmetric Pairs.

Cover
Title page
Acknowledgment
Notations
Chapter 1. Introduction
1.1. History
1.2. The goal
1.3. Main results
1.4. The organization
Part 1. Affine Schur algebras
Chapter 2. Affine Schur algebras via affine Hecke algebras
2.1. Affine Weyl groups
2.2. Parabolic subgroups and cosets
2.3. Affine Schur algebra via Hecke
2.4. Set-valued matrices
2.5. A bijection
2.6. Computation in affine Schur algebra ^{ }_{ , }
2.7. Isomorphism ^{ , }_{ , }≅ ^{ }_{ , }
Chapter 3. Multiplication formula for affine Hecke algebra
3.1. Minimal length representatives
3.2. Multiplication formula for affine Hecke algebra
3.3. An example
Chapter 4. Multiplication formula for affine Schur algebra
4.1. A map
4.2. Algebraic combinatorics for ^{ }_{ , }
4.3. Multiplication formula for ^{ }_{ , }
4.4. Special cases of the multiplication formula
Chapter 5. Monomial and canonical bases for affine Schur algebra
5.1. Bar involution on ^{ }_{ , }
5.2. A standard basis in ^{ }_{ , }
5.3. Multiplication formula using [ ]
5.4. The canonical basis for ^{ }_{ , }
5.5. A leading term
5.6. A semi-monomial basis
5.7. A monomial basis for ^{ }_{ , }
Part 2. Affine quantum symmetric pairs
Chapter 6. Stabilization algebra ̇^{ }_{ } arising from affine Schur algebras
6.1. A BLM-type stabilization
6.2. Stabilization of bar involutions
6.3. Multiplication formula for ̇^{ }_{ }
6.4. Monomial and stably canonical bases for ̇^{ }_{ }
6.5. Isomorphism ̇^{ , }_{ }≅ ̇^{ }_{ }
Chapter 7. The quantum symmetric pair ( _{ }, ^{ }_{ })
7.1. The algebra _{ } of Type A
7.2. The algebra ^{ }_{ }
7.3. The algebra ^{ }_{ } as a subquotient
7.4. Comultiplication on ^{ }_{ }
Chapter 8. Stabilization algebras arising from other Schur algebras.

8.1. Affine Schur algebras of Type
8.2. Monomial and canonical bases for ^{ }_{ , }
8.3. Stabilization algebra of Type
8.4. Stabilization algebra of Type
8.5. Stabilization algebra of Type
Appendix A. Length formulas in symmetrized forms by Zhaobing Fan, Chun-Ju Lai, Yiqiang Li and Li Luo
A.1. Dimension of generalized Schubert varieties
A.2. Length formulas of Weyl groups
Bibliography
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