Abstract
Let [Formula: see text] act multiplicatively on the Laurent polynomial algebra k[x± 1] in n indeterminates x={x1, …,xn}. Consider the initial algebra of the ring of invariants [Formula: see text] with respect to some monomial order. We set a sufficient condition on [Formula: see text] such that each initial algebra is represented by some weight vectors in ℝn. We also show that the condition is necessary in the case where the rank n = 2.
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