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

作者：Howard Benjamin J; McAllister Tyrrell B^*

来源：Journal of Algebraic Combinatorics, 2011, 34(2): 237-249.

DOI：10.1007/s10801-010-0269-x

• Weight ring
• Weight variety
• Cohen-Macaulay ring
• Toric degeneration
• Gelfand-Tsetlin pattern

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.

• 出版日期2011-9