Abstract
A weight ring in type A is the coordinate ring of the GIT quotient of the variety of flags in ℂn modulo a twisted action of the maximal torus in SL(n,ℂ). We show that any weight ring in type A is generated by elements of degree strictly less than the Krull dimension, which is at worst O(n 2). On the other hand, we show that the associated semigroup of Gelfand–Tsetlin patterns can have an essential generator of degree exponential in n.
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Second author supported by the Netherlands Organization for Scientific Research (NWO) Mathematics Cluster DIAMANT.
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Howard, B.J., McAllister, T.B. Degree bounds for type-A weight rings and Gelfand–Tsetlin semigroups. J Algebr Comb 34, 237–249 (2011). https://doi.org/10.1007/s10801-010-0269-x
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DOI: https://doi.org/10.1007/s10801-010-0269-x