JournalscmhVol. 78 , No. 1DOI 10.1007/s000140300008

SAGBI bases in rings of multiplicative invariants

  • Zinovy Reichstein

    University of British Columbia, Vancouver, Canada
SAGBI bases in rings of multiplicative invariants cover

Abstract

Let k be a field and G be a finite subgroup of \GLn(Z)\GL_n(\mathbb Z). We show that the ring of multiplicative invariants k[x1±1,,xn±1]Gk[x_1^{\pm 1}, \dots, x_n^{\pm 1}]^G has a finite SAGBI basis if and only if G is generated by reflections.