Finite-dimensional vertex algebra modules over fixed point differential subfields (Q713391)

R. Borcherds showed that every commutative ring \(A\) with an arbitrary derivation \(D\) has a structure of vertex algebra. Let \(K\) be a differential field with derivation \(D\), \(G\) a finite linear automorphism group of \(K\) which preserves \(D\), and let \(K^G\) be the fixed point subfield of \(K\). The author studies \(K^G\) as a vertex algebra. It is proved that every finite-dimensional indecomposable vertex algebra \(K^G\)-module becomes a \(g\)-twisted vertex algebra \(K\)-module for some \(g\in G\), thus answering in the affirmative to a general conjecture in this special case.