Quivers for $\mathrm {SL}_{2}$ tilting modules
Authors:
Daniel Tubbenhauer and Paul Wedrich
Journal:
Represent. Theory 25 (2021), 440-480
MSC (2020):
Primary 20G05, 20C20; Secondary 16D90, 17B10, 20G40
DOI:
https://doi.org/10.1090/ert/569
Published electronically:
June 3, 2021
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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Additional 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
Keywords:
Modular representation theory,
tilting modules,
diagrammatic algebra,
generators and relations,
Temperley–Lieb,
positive characteristic.
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.
Article copyright:
© Copyright 2021
American Mathematical Society
