Abstract
We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and 1432-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which appeared in previous joint work of the authors with Y. Ren and A. St. Dizier. We apply our formulas to compute Castelnuovo-Mumford regularity of classes of generalized determinantal ideals. In particular, we give combinatorial formulas for the regularities of all one-sided mixed ladder determinantal ideals. We also derive formulas for the regularities of certain Kazhdan-Lusztig ideals, including those coming from open patches of Schubert varieties in Grassmannians. This provides a correction to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri (2015).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 160-191 |
| Number of pages | 32 |
| Journal | Journal of Algebra |
| Volume | 617 |
| DOIs | |
| State | Published - Mar 1 2023 |
| Externally published | Yes |
Bibliographical note
Funding Information:Jenna Rajchgot was partially supported by NSERC Grant RGPIN-2017-05732.Colleen Robichaux was supported by the NSF GRFP under Grant No. DGE 1746047 and NSF RTG Grant No. DMS 1937241.Anna Weigandt was partially supported by Bill Fulton's Oscar Zariski Distinguished Professor Chair funds.
Publisher Copyright:
© 2022 Elsevier Inc.
Keywords
- Castelnuovo-Mumford regularity
- Grassmannian
- Grothendieck polynomial
- Ladder determinantal ideal
- Matrix Schubert variety