Affine Hecke algebras and quantum symmetric pairs
We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplicatio...
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| Hlavní autori: | , , , , |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Providence, Rhode Island
American Mathematical Society
2023
AMS, American Mathematical Society |
| Vydanie: | 1 |
| Edícia: | Memoirs of the American Mathematical Society |
| Predmet: | |
| ISBN: | 9781470456269, 1470456265 |
| ISSN: | 0065-9266, 1947-6221 |
| On-line prístup: | Získať plný text |
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Obsah:
- Acknowledgment -- Notations -- Introduction -- Affine Schur algebras -- Affine Schur algebras via affine Hecke algebras -- Multiplication formula for affine Hecke algebra -- Multiplication formula for affine Schur algebra -- Monomial and canonical bases for affine Schur algebra -- Affine quantum symmetric pairs -- Stabilization algebra <inline-formula content-type="math/mathml"> K ˙ n c \dot {\mathbf {K}}^{\mathfrak {c}}_n </inline-formula> arising from affine Schur algebras -- The quantum symmetric pair <inline-formula content-type="math/mathml"> ( K n , K n c ) (\mathbf {K}_n, \mathbf {K}^{\mathfrak {c}}_n) </inline-formula> -- Stabilization algebras arising from other Schur algebras -- Length formulas in symmetrized forms by Zhaobing Fan, Chun-Ju Lai, Yiqiang Li and Li Luo
- 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 -- Back Cover