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

Tatsuya Horiguchi

Published 2014-04-04, updated 2016-02-08Version 2

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.