Quivers for $\mathrm {SL}_{2}$ tilting modules
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- by Daniel Tubbenhauer and Paul Wedrich
- Represent. Theory 25 (2021), 440-480
- DOI: https://doi.org/10.1090/ert/569
- Published electronically: June 3, 2021
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Abstract:
Using diagrammatic methods, we define a quiver with relations depending on a prime $\mathsf {p}$ and show that the associated path algebra describes the category of tilting modules for $\mathrm {SL}_{2}$ in characteristic $\mathsf {p}$. Along the way we obtain a presentation for morphisms between $\mathsf {p}$-Jones–Wenzl projectors.References
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Bibliographic Information
- Daniel Tubbenhauer
- Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Campus Irchel, Office Y27J32, CH-8057 Zürich, Switzerland
- MR Author ID: 1067860
- ORCID: 0000-0001-7265-5047
- Email: daniel.tubbenhauer@math.uzh.ch
- Paul Wedrich
- Affiliation: Mathematical Sciences Institute, The Australian National University, Hanna Neumann Building, Canberra ACT 2601, Australia
- MR Author ID: 1152159
- ORCID: 0000-0002-2517-7924
- Email: p.wedrich@gmail.com
- Received by editor(s): February 11, 2020
- Received by editor(s) in revised form: November 25, 2020
- Published electronically: June 3, 2021
- Additional Notes: The second author was supported by Australian Research Council grants ‘Braid groups and higher representation theory’ DP140103821 and ‘Low dimensional categories’ DP160103479.
- © Copyright 2021 American Mathematical Society
- Journal: Represent. Theory 25 (2021), 440-480
- MSC (2020): Primary 20G05, 20C20; Secondary 16D90, 17B10, 20G40
- DOI: https://doi.org/10.1090/ert/569
- MathSciNet review: 4273168