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math.RT2025
The elliptic Hall algebra and the double Dyck path algebra
Nicolle Gonzalez, Eugene Gorsky, Jose Simental
We show that the positive half of the elliptic Hall algebra is embedded as a natural spherical subalgebra inside the double Dyck path algebra $\mathbb{B}_{q…
math.RT2022
Extremal tensor products of Demazure crystals
Sami Assaf, Anne Dranowski, Nicolle Gonzalez
Demazure crystals are subcrystals of highest weight irreducible -crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal…
math.RT2018
Categorical Bernstein Operators and the Boson-Fermion Correspondence
Nicolle Gonzalez
We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to inf…