Torus Equivariant Cohomology for the $\Delta$-Springer Fiber

Abstract

We define a torus $U \subset T = (\mathbb{C}^\times)^K$ which acts on the $\Delta$-Springer varieties $Y_{n,\lambda,s}$ defined by Griffin-Levinson-Woo and give a Borel-style presentation for the equivariant cohomology ring $H^*_U(Y_{n,\lambda,s})$. Our presentation arises from the orbit harmonics deformation technique, and uses methods of Chou-Matsumura-Rhoades and Abe-Horiguchi.