| Description |
1 online resource (176 pages) |
| Series |
Memoirs of the American Mathematical Society, 1947-6221 ; Volume 235, Number 1109 (fourth of 5 numbers) |
|
Memoirs of the American Mathematical Society ; Volume 235, no. 1109 (fourth of 5 numbers)
|
| Contents |
Cover -- Title page -- Chapter 1. Introduction -- 1.1. The Kronecker problem -- 1.2. The basis-theoretic version of the Kronecker problem -- 1.3. Canonical bases connect quantum Schur-Weyl duality with RSK -- 1.4. The nonstandard quantum group and Hecke algebra -- 1.5. Towards an upper canonical basis for \nsbr{ }̂{\tsr } -- 1.6. The approach of Adsul, Sohoni, and Subrahmanyam -- 1.7. A global crystal basis for \nsbr{ }_{ } -- 1.8. Organization -- Chapter 2. Basic concepts and notation -- 2.1. General notation -- 2.2. Tensor products |
|
2.3. Words and tableaux2.4. Cells -- 2.5. Comodules -- 2.6. Dually paired Hopf algebras -- Chapter 3. Hecke algebras and canonical bases -- 3.1. The upper canonical basis of â??() -- 3.2. Cells in type -- Chapter 4. The quantum group _{ }() -- 4.1. The quantized enveloping algebra \Uq -- 4.2. FRT-algebras -- 4.3. The quantum coordinate algebra Ã?(_{ }()) -- 4.4. The quantum determinant and the Hopf algebra Ã?(_{ }()) -- 4.5. A reduction system for Ã?(_{ }()) -- 4.6. Compactness, unitary transformations |
|
4.7. Representations of _{ }()Chapter 5. Bases for _{ }() modules -- 5.1. Gelfand-Tsetlin bases and Clebsch-Gordon coefficients -- 5.2. Crystal bases -- 5.3. Global crystal bases -- 5.4. Projected based modules -- 5.5. Tensor products of based modules -- Chapter 6. Quantum Schur-Weyl duality and canonical bases -- 6.1. Commuting actions on \bT= ̂{\tsr } -- 6.2. Upper canonical basis of \bT -- 6.3. Graphical calculus for _{ }(\glâ??)-modules -- Chapter 7. Notation for _{ }()Ã? _{ }() |
|
Chapter 8. The nonstandard coordinate algebra (â?³_{ }())8.1. Definition of Ã?(_{ }(\nsbr{ })) -- 8.2. Nonstandard symmetric and exterior algebras -- 8.3. Explicit product formulae -- 8.4. Examples and computations for Ã?(_{ }(\nsbr{ })) -- Chapter 9. Nonstandard determinant and minors -- 9.1. Definitions -- 9.2. Nonstandard minors in the two-row case -- 9.3. Symmetry of the determinants and minors -- 9.4. Formulae for nonstandard minors -- Chapter 10. The nonstandard quantum groups _{ }() and _{ }() -- 10.1. Hopf structure |
|
10.2. Compact real form10.3. Complete reducibility -- Chapter 11. The nonstandard Hecke algebra â??áæ£ -- 11.1. Definition of \nsHáæ£ and basic properties -- 11.2. Semisimplicity of \field\nsHáæ£ -- 11.3. Representation theory of ²â??áæ£ -- 11.4. Some representation theory of \nsHáæ£ -- 11.5. The sign representation in the canonical basis -- 11.6. The algebra \nsHâ?? -- 11.7. A canonical basis of \nsHâ?? -- 11.8. The algebra \nsHâ?? -- Chapter 12. Nonstandard Schur-Weyl duality -- 12.1. Nonstandard Schur-Weyl duality |
| Bibliography |
Includes bibliographical references |
| Notes |
English |
|
Print version record |
| Subject |
Combinatorial analysis.
|
|
Kronecker products.
|
|
Combinatorial analysis
|
|
Kronecker products
|
| Form |
Electronic book
|
| Author |
Mulmuley, Ketan, author
|
|
Sohoni, Milind, 1969- author.
|
| ISBN |
9781470422271 |
|
1470422271 |
|
