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|2 23/eng/20230313
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|a Fan, Zhaobing.
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|a Affine Hecke algebras and quantum symmetric pairs.
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|a Providence :
|b American Mathematical Society,
|c 2023.
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| 300 |
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|a 1 online resource.
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|b txt
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|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
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|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
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|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
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|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
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| 533 |
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|a Electronic reproduction.
|b Ann Arbor, MI
|n Available via World Wide Web.
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| 650 |
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|a Hecke algebras.
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| 650 |
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|a Mathematics
|v Periodicals.
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|a ProQuest (Firm)
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|z 9781470456269
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