Torus Equivariant Cohomology for the $\mathrm{\Delta }$-Springer Fiber

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