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arXiv · 2108.06864

Standard monomials and invariant theory for arc spaces I: general linear group

Andrew R. Linshaw·Bailin Song
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Abstract

This is the first in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we construct a standard monomial basis for the arc space of the determinantal variety over $K$. As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the general linear group.

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Andrew R. Linshaw, Bailin Song. 2021-08-16. Standard monomials and invariant theory for arc spaces I: general linear group. https://doi.org/10.1142/s021919972350013x

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