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Jonathan Elmer

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Preprint Jul 2026

Semi-Invariants of a Matrix and Covector

We prove the following theorem: let $\mathcal{M}_d$ denote the set of $d \times d$ matrices over an infinite field $K$, and let ${(K^d)^*}$ be the set of row vectors. Define an action of $\mathrm{SL}_d(K)$ on $X:= \mathcal{M}_d \oplus (K^d)^*$ by \[ g \cdot (A,\phi) = (gAg^{-1}, \phi g^{-1}).\] Then $K[X]^{\mathrm{SL}_...

Jonathan Elmer · 0 citations