Degree bounds for type-A weight rings and Gelfand--Tsetlin semigroups

Details Degree bounds for type-A weight rings and Gelfand--Tsetlin semigroups Degree bounds for type-A weight rings and Gelfand--Tsetlin semigroups

2008-12-03

arxiv.org/abs/0812.0826v2

Mathematics

Algebraic Geometry

12 pages, 1 figure, v2: hyperref package options changed to suit non-pdf latex

Scientific paper

A weight ring in type A is the coordinate ring of the GIT quotient of the variety of flags in $\C^n$ 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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