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arXiv · 2501.04605

Big Algebra in Type $A$ for the Coordinate Ring of the Matrix Space

Nhok Tkhai Shon Ngo
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Abstract

In this paper, we consider the big algebra recently introduced by Hausel for the $\mathrm{GL}_n$-action on the coordinate ring of the matrix space $\mathrm{Mat}(n,r)$. In particular, we obtain explicit formulas for the big algebra generators in terms of differential operators with polynomial coefficients. We show that big algebras in type $A$ are commutative and relate them to the Bethe subalgebra in the Yangian $\operatorname{Y}(\mathfrak{gl}_{n})$. We apply these results to big algebras of symmetric powers of the standard representation of $\mathrm{GL}_n$.

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BibTeXRIS

Nhok Tkhai Shon Ngo. 2025-01-08. Big Algebra in Type $A$ for the Coordinate Ring of the Matrix Space. https://doi.org/10.3842/sigma.2026.024

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