Degree bounds for type-A weight rings and Gelfand-Tsetlin semigroups
Benjamin J. Howard
and Tyrrell B. McAllister
DOI: 10.1007/s10801-010-0269-x
Abstract
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.
Pages: 237–249
Keywords: keywords weight ring; weight variety; Cohen-Macaulay ring; toric degeneration; Gelfand-tsetlin pattern
Full Text: PDF
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3. De Loera, J.A., McAllister, T.B.: Vertices of Gelfand-Tsetlin polytopes. Discrete Comput. Geom. 32(4), 459-470 (2004)
4. Derksen, H., Kraft, H.: Constructive Invariant Theory, Algèbre non commutative, groupes quantiques et invariants, Reims,
1995. Sémin. Congr., vol. 2, pp. 221-244. Soc. Math. France, Paris (1997)
5. Dolgachev, I.: Lectures on Invariant Theory. London Mathematical Society Lecture Note Series, vol.
296. Cambridge University Press, Cambridge (2003)
6. Dolgachev, I., Ortland, D.: Point sets in projective spaces and theta functions. Astérisque 165, 210 (1988)
7. Eisenbud, D.: Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics, vol.
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11. Howard, B.J.: Matroids and geometric invariant theory of torus actions on flag spaces. J. Algebra 312(1), 527-541 (2007)
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