This paper proves the existence of RGD-systems dependent on Weyl-invariant commutation relations, indicating new complexities.
In this paper we prove that an RGD-system over F₂ with prescribed commutation relations exists if and only if the commutation relations are Weyl-invariant and can be realized in the group U₊ . This result gives us a machinery to produce new examples of RGD-systems with complicated commutation relations. We also discuss some applications of this result.
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Sebastian Bischof (2025) studied this question.
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