Lifting polynomial representations of SL2(pr) from 𝔽p to ℤ/psℤ

Chris Parker; Martin Van Beek

doi:10.1090/proc/17599

Lifting polynomial representations of SL₂(p^r) from 𝔽_p to ℤ/p^sℤ

Chris Parker
, Martin Van Beek^*

^*Corresponding author for this work

Mathematics

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

3 Downloads (Pure)

Abstract

We describe all of the irreducible polynomial 𝔽_pSL₂(p^r) representations which lift to (ℤ/p^sℤ)SL₂(p^r) representations for s > 1, observing that they almost never do. We also show that two related indecomposable 𝔽_pSL₂(p^r) representations cannot be lifted to ℤ/p^sℤ representations for s > 1.

Original language	English
Journal	Proceedings of the American Mathematical Society
Early online date	21 Apr 2026
DOIs	https://doi.org/10.1090/proc/17599
Publication status	E-pub ahead of print - 21 Apr 2026

Keywords

Basic representations
modular representation theory
p-adic representations

Access to Document

10.1090/proc/17599Licence: None: All rights reserved

ParkerC2025Lifting_AAMAccepted author manuscript, 387 KBLicence: Creative Commons: Attribution (CC BY)

Cite this

@article{b2fa4396a11d4dd2b5aee3cd32bc134e,

title = "Lifting polynomial representations of SL2(pr) from 𝔽p to ℤ/psℤ",

abstract = "We describe all of the irreducible polynomial 𝔽pSL2(pr) representations which lift to (ℤ/psℤ)SL2(pr) representations for s > 1, observing that they almost never do. We also show that two related indecomposable 𝔽pSL2(pr) representations cannot be lifted to ℤ/psℤ representations for s > 1.",

keywords = "Basic representations, modular representation theory, p-adic representations",

author = "Chris Parker and \{Van Beek\}, Martin",

year = "2026",

month = apr,

day = "21",

doi = "10.1090/proc/17599",

language = "English",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Lifting polynomial representations of SL2(pr) from 𝔽p to ℤ/psℤ

AU - Parker, Chris

AU - Van Beek, Martin

PY - 2026/4/21

Y1 - 2026/4/21

N2 - We describe all of the irreducible polynomial 𝔽pSL2(pr) representations which lift to (ℤ/psℤ)SL2(pr) representations for s > 1, observing that they almost never do. We also show that two related indecomposable 𝔽pSL2(pr) representations cannot be lifted to ℤ/psℤ representations for s > 1.

AB - We describe all of the irreducible polynomial 𝔽pSL2(pr) representations which lift to (ℤ/psℤ)SL2(pr) representations for s > 1, observing that they almost never do. We also show that two related indecomposable 𝔽pSL2(pr) representations cannot be lifted to ℤ/psℤ representations for s > 1.

KW - Basic representations

KW - modular representation theory

KW - p-adic representations

UR - https://arxiv.org/pdf/2411.16379

U2 - 10.1090/proc/17599

DO - 10.1090/proc/17599

M3 - Article

SN - 0002-9939

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -