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

Format:

Book

Author/Creator:

Blasiak, Jonah, 1982-

Contributor:

Mulmuley, Ketan.

Sohoni, Milind, 1969-

Series:

Memoirs of the American Mathematical Society ; v. 1109.

Memoirs of the American Mathematical Society, 1947-6221 ; v. 1109

Language:

English

Subjects (All):

Combinatorial analysis.

Kronecker products.

Physical Description:

1 online resource (ix, 160 pages : illustrations).

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2015.

System Details:

Mode of access : World Wide Web

text file

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 $

Notes:

"Volume 235, number 1109 (fourth of 5 numbers), May 2015."

Includes bibliographical references (pages 157-160).

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

Description based on print version record.

Other Format:

Print version: Blasiak, Jonah, 1982- Geometric complexity theory IV :

ISBN:

9781470422271

Access Restriction:

Restricted for use by site license.