The $S^{1}$-equivariant cohomology rings of $(n - k, k)$ Springer varieties

Abstract

The main result of this note gives an explicit presentation of the $S^{1}$-equivariant cohomology ring of the $(n-k, k)$ Springer variety (in type $A$) as a quotient of a polynomial ring by an ideal $I$, in the spirit of the well-known Borel presentation of the cohomology of the flag variety.