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Title: Gröbner bases, symmetric matrices, and type C Kazhdan–Lusztig varieties
Abstract We 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.  more » « less
Award ID(s):
1855598
PAR ID:
10494811
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Journal of the London Mathematical Society
Date Published:
Journal Name:
Journal of the London Mathematical Society
Volume:
109
Issue:
2
ISSN:
0024-6107
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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