TY  - BOOK
AU  - Blasiak,Jonah
AU  - Mulmuley,Ketan
AU  - Sohoni,Milind
TI  - Geometric complexity theory IV: nonstandard quantum group for the Kronecker problem 
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470422271 (online)
AV  - QA164 .B575 2015
U1  - 516/.13 23
PY  - 2015///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Combinatorial analysis
KW  - Kronecker products
N1  - Includes bibliographical references; 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 $; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2015
UR  - http://www.ams.org/memo/1109/
UR  - http://dx.doi.org/10.1090/memo/1109
ER  -