Crystal Structure on the Category of Modules over Colored Planar Rook Algebra
arXiv:1303.0410
Abstract
Colored planar rook algebra is a semigroup algebra in which the basis element has a diagrammatic description. The category of finite dimensional modules over this algebra is completely reducible and suitable functors are defined on this category so that it admits a crystal structure in the sense of Kashiwara. We show that the category and functors categorify the crystal bases for the polynomial representations of quantized enveloping algebra .
17 pages, 1 figure