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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 thewell-known Borel presentation of the cohomology of the flag variety.

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