Lifting polynomial representations of SL<sub>2</sub>(<i>p</i><sup>r</sup>) from <i><sub>p</sub></i> to ℤ/<i>p</i><sup>s</sup>ℤ
We describe all of the irreducible polynomial <i style="background-color: rgb(255, 255, 238);"><sub>p</sub></i>SL<sub style="background-color: rgb(255, 255, 238);">2</sub>(<i style="background-color: rgb(255, 255, 238);">p</i><sup style="background-color: rgb(255, 255, 238);">r</sup>) representations which lift to (ℤ/<i style="background-color: rgb(255, 255, 238);">p</i><sup style="background-color: rgb(255, 255, 238);">s</sup>ℤ)SL<sub style="background-color: rgb(255, 255, 238);">2</sub>(<i style="background-color: rgb(255, 255, 238);">p</i><sup style="background-color: rgb(255, 255, 238);">r</sup>) representations for <i>s </i>> 1, observing that they almost never do. We also show that two related indecomposable <i style="background-color: rgb(255, 255, 238);"><sub>p</sub></i>SL<sub style="background-color: rgb(255, 255, 238);">2</sub>(<i style="background-color: rgb(255, 255, 238);">p</i><sup style="background-color: rgb(255, 255, 238);">r</sup>) representations cannot be lifted to ℤ/<i style="background-color: rgb(255, 255, 238);">p</i><sup style="background-color: rgb(255, 255, 238);">s</sup>ℤ representations for <i>s </i>> 1.
Publication Details
- Journal
- University of Birmingham Research Portal (University of Birmingham)
- Published
- 2025-11-25
- Primary Topic
- Advanced Algebra and Geometry
- Type
- article
- Field-Weighted Citation Impact
- 0.00