Affine Hecke algebras and quantum symmetric pairs.

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Bibliographic Details
Main Author: Fan, Zhaobing
Corporate Author: ProQuest (Firm)
Format: Electronic eBook
Language:English
Published: Providence : American Mathematical Society, 2023.
Subjects:
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

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505 0 |a 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 ^{ , }_{ , }E ^{ }_{ , } -- Chapter 3. Multiplication formula for affine Hecke algebra 
505 8 |a 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 
505 8 |a 5.6. A semi-monomial basis -- 5.7. A monomial basis for ^{ }_{ , } -- Part 2. Affine quantum symmetric pairs -- Chapter 6. Stabilization algebrȧ ^{ }_{ } arising from affine Schur algebras -- 6.1. A BLM-type stabilization -- 6.2. Stabilization of bar involutions -- 6.3. Multiplication formula foṙ ^{ }_{ } -- 6.4. Monomial and stably canonical bases foṙ ^{ }_{ } -- 6.5. Isomorphisṁ ^{ , }_{ }Ė ^{ }_{ } -- Chapter 7. The quantum symmetric pair ( _{ }, ^{ }_{ }) -- 7.1. The algebra _{ } of Type A -- 7.2. The algebra ^{ }_{ } -- 7.3. The algebra ^{ }_{ } as a subquotient 
505 8 |a 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 -- Back Cover 
533 |a Electronic reproduction.  |b Ann Arbor, MI  |n Available via World Wide Web. 
650 0 |a Hecke algebras. 
650 0 |a Mathematics  |v Periodicals. 
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