KRS and determinantal ideals
摘要
The first sections contain a survey of the application of the Knuth-Robinson-Schensted corerspondence to the computation of Groebner bases of determinantal ideals. We also set up a conceptual framework for this application in terms of so-called "KRS invariants". Then we show that the initial ideal of a determinantal ideal "defined by shape" is given by its KRS image. We furthermore characterize those among these ideals that even have a Groebner basis of products of minors, and show that they can be characterized in terms of Greene's KRS invariants. Furthermore it is shown that for the ideal generated by all t-minors the formation of initial ideal and symbolic power commutes. The last section contains a discussion of potential KRS invariants related to so-called 1-cogenerated ideals.
引用
@article{arxiv.math/0005260,
title = {KRS and determinantal ideals},
author = {Winfried Bruns and Aldo Conca},
journal= {arXiv preprint arXiv:math/0005260},
year = {2007}
}
备注
22 pages, uses epic, eepic