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

  • Authors:

  • Benjamin J. Howard;Tyrrell B. Mcallister

  • Affiliations:

  • Mathematics Department, University of Michigan, Ann Arbor, USA 48109;Department of Mathematics, University of Wyoming, Laramie, USA 82071-2000

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2011

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Abstract

A weight ring in type A is the coordinate ring of the GIT quotient of the variety of flags in 驴 n modulo a twisted action of the maximal torus in SL(n,驴). 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.