%0 Journal Article
%T The equivariant cohomology rings of Peterson varieties
%A Yukiko Fukukawa
%A Megumi Harada
%A Mikiya Masuda
%J Mathematics
%D 2013
%I arXiv
%R 10.2969/jmsj/06731147
%X The main result of this note is an efficient presentation of the $S^1$-equivariant cohomology ring of Peterson varieties (in type $A$) as a quotient of a polynomial ring by an ideal $\mathcal{J}$, in the spirit of the well-known Borel presentation of the cohomology of the flag variety. Our result simplifies previous presentations given by Harada-Tymoczko and Bayegan-Harada. In particular, our result gives an affirmative answer to a conjecture of Bayegan and Harada that the defining ideal $\mathcal{J}$ is generated by quadratics.
%U http://arxiv.org/abs/1310.8643v2