Abstract
Working in a polynomial ring (Formula presented.), where (Formula presented.) is an arbitrary commutative ring with 1, we consider the (Formula presented.) th Veronese subalgebras (Formula presented.), as well as natural (Formula presented.) -submodules (Formula presented.) inside (Formula presented.). We develop and use characteristic-free theory of Schur functors associated to ribbon skew diagrams as a tool to construct simple (Formula presented.) -equivariant minimal free (Formula presented.) -resolutions for the quotient ring (Formula presented.) and for these modules (Formula presented.). These also lead to elegant descriptions of (Formula presented.) for all (Formula presented.) and (Formula presented.) for any pair of these modules (Formula presented.).
| Original language | English |
|---|---|
| Article number | e12848 |
| Journal | Journal of the London Mathematical Society |
| Volume | 109 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2024 |
Bibliographical note
Publisher Copyright:© 2023 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
Funding
The authors thank Francesca Gandini for helpful conversations, and Darij Grinberg for helpful edits, including a shortening of the proof of Proposition 3.6(iii) . They thank an anonymous referee for helpful edits. The first author was partially supported by NSF Grant DMS‐1745638, third and fourth authors by NSF Grant DMS‐2053288, and the fifth author by NSF Grant DMS‐2202871.
| Funders | Funder number |
|---|---|
| National Science Foundation Arctic Social Science Program | DMS‐2202871, 2053288, DMS‐1745638, DMS‐2053288 |
ASJC Scopus subject areas
- General Mathematics
Fingerprint
Dive into the research topics of 'Equivariant resolutions over Veronese rings'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver