RELATION BETWEEN CATEGORIES OF REPRESENTATIONS OF THE SUPER-YANGIAN OF A SPECIAL LINEAR LIE SUPERALGEBRA AND QUANTUM LOOP SUPERALGEBRA

摘要

Using the approach developed by Gautam and Toledano Laredo, we introduce analogues of the category O for representations of the Yangian Y-(h) over bar(A(m, n)) of a special linear Lie superalgebra and the quantum loop superalgebra U-q(LA(m, n)). We investigate the relation between them and conjecture that these categories are equivalent.