Affiliation:
1. Department of Mathematics Washington University in St. Louis St. Louis Missouri USA
2. School of Mathematical Sciences Queen Mary University of London London UK
3. Department of Mathematics and Statistics McMaster University Hamilton ON Canada
4. Department of Mathematics and Statistical Science University of Idaho Moscow Idaho USA
Abstract
AbstractWe study a class of combinatorially defined polynomial ideals that are generated by minors of a generic symmetric matrix. Included within this class are the symmetric determinantal ideals, the symmetric ladder determinantal ideals, and the symmetric Schubert determinantal ideals of A. Fink, J. Rajchgot, and S. Sullivant. Each ideal in our class is a type C analog of a Kazhdan–Lusztig ideal of A. Woo and A. Yong; that is, it is the scheme‐theoretic defining ideal of the intersection of a type C Schubert variety with a type C opposite Schubert cell, appropriately coordinatized. The Kazhdan–Lusztig ideals that arise are exactly those where the opposite cell is 123‐avoiding. Our main results include Gröbner bases for these ideals, prime decompositions of their initial ideals (which are Stanley–Reisner ideals of subword complexes), and combinatorial formulas for their multigraded Hilbert series in terms of pipe dreams.
Funder
National Science Foundation
Natural Sciences and Engineering Research Council of Canada
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