A categorification of the Vandermonde determinant

In the spirit of Bar-Natan's construction of Khovanov homology, we give a categorification of the Vandermonde determinant. Given a sequence of positive integers (x) over right arrow = (x(1), . . . , x(n)), we construct a complex of colored smoothings of the two-strand torus link T-2,T-n in the shape of the Bruhat order on S-n, and apply a topological quantum field theory (TQFT) to obtain a chain complex whose Euler characteristic is equal to the Vandermonde determinant evaluated at (x) over right arrow. A generalization to arbitrary link diagrams is given, yielding categorifications of certain generalized Vandermonde determinants.