Anne Dranowski
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View article: Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras
Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras Open
Leveraging skew Howe duality, we show that Lawson-Lipshitz-Sarkar's spectrification of Khovanov's arc algebra gives rise to 2-representations of categorified quantum groups over $\mathbb{F}_2$ that we call spectral 2-representations. These…
View article: Extremal Tensor Products of Demazure Crystals
Extremal Tensor Products of Demazure Crystals Open
Demazure crystals are subcrystals of highest weight irreducible $$\mathfrak {g}$$ -crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal, and give a local characterization for exactly when …
View article: Computing fusion products of MV cycles using the Mirković–Vybornov isomorphism
Computing fusion products of MV cycles using the Mirković–Vybornov isomorphism Open
The fusion of two Mirković–Vilonen cycles is a degeneration of their product, defined using the Beilinson–Drinfeld Grassmannian. In this paper, we put in place a conceptually elementary approach to computing this product in type A . We do …
View article: Extremal tensor products of Demazure crystals
Extremal tensor products of Demazure crystals Open
Demazure crystals are subcrystals of highest weight irreducible $\mathfrak{g}$-crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal, and give a local characterization for exactly when the te…
View article: Heaps, crystals, and preprojective algebra modules
Heaps, crystals, and preprojective algebra modules Open
Fix a simply-laced semisimple Lie algebra. We study the crystal $ B(nλ)$, were $λ$ is a dominant minuscule weight and $n$ is a natural number. On one hand, $B(nλ)$ can be realized combinatorially by height $n$ reverse plane partitions on a…
View article: Comparing two perfect bases
Comparing two perfect bases Open
We study a class of varieties which generalize the classical orbital varieties of Joseph. We show that our generalized orbital varieties are the irreducible components of a Mirkovic-Vybornov slice to a nilpotent orbit, and can be labeled b…