Equivariant resolutions over Veronese rings

Ayah Almousa; Michael Perlman; Alexandra Pevzner; Victor Reiner; Keller VandeBogert

doi:10.1112/jlms.12848

Equivariant resolutions over Veronese rings

Ayah Almousa, Michael Perlman, Alexandra Pevzner, Victor Reiner, Keller VandeBogert

Mathematics

Research output: Contribution to journal › Article › peer-review

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 (US)
Article number	e12848
Journal	Journal of the London Mathematical Society
Volume	109
Issue number	1
DOIs	https://doi.org/10.1112/jlms.12848
State	Published - Jan 2024

Bibliographical note

Publisher Copyright:
© 2023 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.

Access

10.1112/jlms.12848

OpenUrl availability

Full text

Cite this

@article{70f0dd8761234540ad17da7c7d6ea307,

title = "Equivariant resolutions over Veronese rings",

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.).",

author = "Ayah Almousa and Michael Perlman and Alexandra Pevzner and Victor Reiner and Keller VandeBogert",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors. Journal of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

year = "2024",

month = jan,

doi = "10.1112/jlms.12848",

language = "English (US)",

volume = "109",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "Oxford University Press",

number = "1",

}

TY - JOUR

T1 - Equivariant resolutions over Veronese rings

AU - Almousa, Ayah

AU - Perlman, Michael

AU - Pevzner, Alexandra

AU - Reiner, Victor

AU - VandeBogert, Keller

PY - 2024/1

Y1 - 2024/1

N2 - 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.).

AB - 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.).

UR - http://www.scopus.com/inward/record.url?scp=85181201815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85181201815&partnerID=8YFLogxK

U2 - 10.1112/jlms.12848

DO - 10.1112/jlms.12848

M3 - Article

AN - SCOPUS:85181201815

SN - 0024-6107

VL - 109

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

M1 - e12848

ER -

Equivariant resolutions over Veronese rings

Abstract

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this