  We study Hardy inequalities for antisymmetric functions in three different
settings: euclidean space, torus and the integer lattice. In particular, we
show that under the antisymmetric condition the sharp constant in Hardy
inequality increases substantially and grows as d^4 as d \rightarrow \infty in
all cases. As a side product, we prove Hardy inequality on a domain whose
boundary forms a corner at the point of singularity x=0.
