SAGBI bases in rings of multiplicative invariants
SAGBI bases in rings of multiplicative invariants
Let k be a field and G be a finite subgroup of \operatorname{GL}_n(\mathbb Z) . We show that the ring of multiplicative invariants k[x_1^{\pm 1}, \dots, x_n^{\pm 1}]^G has a finite SAGBI basis if and only if G is generated by reflections.