Abstract:In this paper, we calculate the combinatorial rank of the positive part [Formula: see text] of the multiparameter version of the small Lusztig quantum group, where [Formula: see text] is a simple Lie algebra of type [Formula: see text]. Supposing that the main parameter of quantization [Formula: see text] has multiplicative order [Formula: see text], where [Formula: see text] is finite, [Formula: see text], we prove that the combinatorial rank equals 3.
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