Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414761 | Journal of Algebra | 2014 | 21 Pages |
Abstract
We give a realization of the level zero fundamental representations W(Ïk) of the quantum affine algebra Uqâ²(g), when g has a maximal parabolic subalgebra of type Cn. We define a semisimple Uqâ²(g)-module structure on Î(V)â2 in terms of q-deformed Clifford generators, where Î(V) is the exterior algebra generated by the dual natural representation V of Uq(sln). We show that each W(Ïk) appears in Î(V)â2 (not necessarily multiplicity-free). As a byproduct, we obtain a simple description of the crystal of W(Ïk) in terms of nÃ2 binary matrices and their (sln,sl2)-bicrystal structure.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jae-Hoon Kwon,