Geometric complexity theory IV : [electronic resource] nonstandard quantum group for the Kronecker problem / Jonah Blasiak, Ketan D. Mulmuley, Milind Sohoni.

By: Blasiak, Jonah, 1982-Contributor(s): Mulmuley, Ketan | Sohoni, Milind, 1969-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 1109Publisher: Providence, Rhode Island : American Mathematical Society, 2015Description: 1 online resource (pages cm.)Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470422271 (online)Subject(s): Combinatorial analysis | Kronecker productsAdditional physical formats: Geometric complexity theory IV :DDC classification: 516/.13 LOC classification: QA164 | .B575 2015Online resources: Contents | Contents
Contents:
Chapter 1. Introduction Chapter 2. Basic concepts and notation Chapter 3. Hecke algebras and canonical bases Chapter 4. The quantum group $GL_q(V)$ Chapter 5. Bases for $GL_q(V)$ modules Chapter 6. Quantum Schur-Weyl duality and canonical bases Chapter 7. Notation for $GL_q(V) \times GL_q(W)$ Chapter 8. The nonstandard coordinate algebra $\mathscr {O}(M_q(\check {X}))$ Chapter 9. Nonstandard determinant and minors Chapter 10. The nonstandard quantum groups $GL_q(\check {X})$ and $\texttt {U}_q(\check {X})$ Chapter 11. The nonstandard Hecke algebra $\check {\mathscr {H}}_r$ Chapter 12. Nonstandard Schur-Weyl duality Chapter 13. Nonstandard representation theory in the two-row case Chapter 14. A canonical basis for $\check {Y}_\alpha $ Chapter 15. A global crystal basis for two-row Kronecker coefficients Chapter 16. Straightened NST and semistandard tableaux Chapter 17. A Kronecker graphical calculus and applications Chapter 18. Explicit formulae for Kronecker coefficients Chapter 19. Future work Appendix A. Reduction system for ${\mathscr {O}}(M_q(\check {X}))$ Appendix B. The Hopf algebra ${\mathscr {O}}_{q}^\tau $
Item type: E-BOOKS
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Chapter 1. Introduction Chapter 2. Basic concepts and notation Chapter 3. Hecke algebras and canonical bases Chapter 4. The quantum group $GL_q(V)$ Chapter 5. Bases for $GL_q(V)$ modules Chapter 6. Quantum Schur-Weyl duality and canonical bases Chapter 7. Notation for $GL_q(V) \times GL_q(W)$ Chapter 8. The nonstandard coordinate algebra $\mathscr {O}(M_q(\check {X}))$ Chapter 9. Nonstandard determinant and minors Chapter 10. The nonstandard quantum groups $GL_q(\check {X})$ and $\texttt {U}_q(\check {X})$ Chapter 11. The nonstandard Hecke algebra $\check {\mathscr {H}}_r$ Chapter 12. Nonstandard Schur-Weyl duality Chapter 13. Nonstandard representation theory in the two-row case Chapter 14. A canonical basis for $\check {Y}_\alpha $ Chapter 15. A global crystal basis for two-row Kronecker coefficients Chapter 16. Straightened NST and semistandard tableaux Chapter 17. A Kronecker graphical calculus and applications Chapter 18. Explicit formulae for Kronecker coefficients Chapter 19. Future work Appendix A. Reduction system for ${\mathscr {O}}(M_q(\check {X}))$ Appendix B. The Hopf algebra ${\mathscr {O}}_{q}^\tau $

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2015

Mode of access : World Wide Web

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