Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Uwe Nagel
We study a class of determinantal ideals called skew tableau ideals, which are generated by t x t minors in a subset of a symmetric matrix of indeterminates. The initial ideals have been studied in the 2 x 2 case by Corso, Nagel, Petrovic and Yuen. Using liaison techniques, we have extended their results to include the original determinantal ideals in the 2 x 2 case, as well as special cases of the ideals in the t x t case. In particular, for any skew tableau ideal of this form, we have defined an elementary biliaison between it and one with a simpler structure. Repeated applications of this result show that these skew tableau ideals are glicci, and thus Cohen-Macaulay.
A number of other classes of ideals have been studied using similar techniques, and these depend on a technical lemma involving determinantal calculations. We have uncovered an error in this result, and have used the straightening law for minors of a matrix to establish a new determinantal relation. This new tool fixes the gaps in the previous papers and is a critical step in our own analysis of skew tableau ideals.
Robinson, Bill, "DETERMINANTAL IDEALS FROM SYMMETRIZED SKEW TABLEAUX" (2015). Theses and Dissertations--Mathematics. 29.