Geodesic
Degree bounds for type-A weight rings and Gelfand--Tsetlin semigroups
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 2, pp. 237-249.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A weight ring in type A is the coordinate ring of the GIT quotient of the variety of flags in $\Bbb C ^{ n }$ modulo a twisted action of the maximal torus in $SL( n,\Bbb C)$. 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 $n$.
Keywords: keywords weight ring, weight variety, Cohen-Macaulay ring, toric degeneration, Gelfand-tsetlin pattern 
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     author = {Howard, Benjamin J. and McAllister, Tyrrell B.},
     title = {Degree bounds for {type-A} weight rings and {Gelfand--Tsetlin} semigroups},
     journal = {Journal of Algebraic Combinatorics},
     pages = {237--249},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_2_a3/}
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Howard, Benjamin J.; McAllister, Tyrrell B. Degree bounds for type-A weight rings and Gelfand--Tsetlin semigroups. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 2, pp. 237-249. http://geodesic.mathdoc.fr/item/JAC_2011__34_2_a3/