2023
DOI: 10.1142/s021919972350013x
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Standard monomials and invariant theory for arc spaces I: General linear group

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 [Formula: see text], we construct a standard monomial basis for the arc space of the determinantal variety over [Formula: see text]. 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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