Super duality and Crystal bases for quantum orthosymplectic superalgebras
| Autor: | Kwon, Jae-Hoon |
|---|---|
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Int. Math. Res. Not. IMRN 2015, no. 23, 12620-12677 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1093/imrn/rnv076 |
| Popis: | We introduce a semisimple tensor category $\mc{O}^{int}_q(m|n)$ of modules over an quantum ortho-symplectic superalgebra. It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical (super) algebra of type $B_{m+n}$, $C_{m+n}$, $D_{m+n}$ or $B(0,m+n)$ from a viewpoint of super duality. We classify the irreducible modules in $\mc{O}^{int}_q(m|n)$ and show that an irreducible module in $\mc{O}^{int}_q(m|n)$ has a unique crystal base in case of type $B$ and $C$. An explicit description of the crystal graph is given in terms of a new combinatorial object called ortho-symplectic tableaux. Comment: 53 pages, Sections 3 and 4 have been revised |
| Databáze: | arXiv |
| Externí odkaz: |
|