Eugene Gorsky

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20242026

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math.AG2025

Splicing braid varieties

Eugene Gorsky, Soyeon Kim, Tonie Scroggin +1

For a positive braid $β \in Br_{k}^{+}$ , we consider the braid variety $X (β)$ . We define a family of open sets $U_{r, w}$ in $X (β)$ , where $w \in S_{k}$ is a permut…

math.AG2025

Splicing skew shaped positroids

Eugene Gorsky, Soyeon Kim, Tonie Scroggin +1

Skew shaped positroids (or skew shaped positroid varieties) are certain Richardson varieties in the flag variety that admit a realization as explicit subvarieties of the Grassmanni…

math.RT2025

The elliptic Hall algebra and the double Dyck path algebra

Nicolle Gonzalez, Eugene Gorsky, Jose Simental

We show that the positive half $E_{q, t}^{>}$ of the elliptic Hall algebra is embedded as a natural spherical subalgebra inside the double Dyck path algebra $\mathbb{B}_{q…