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THE CENTER OF SL2 TILTING MODULES

Part of: Linear algebraic groups and related topics Lie algebras and Lie superalgebras Representation theory of groups

Published online by Cambridge University Press:  05 March 2021

DANIEL TUBBENHAUER  and
PAUL WEDRICH
DANIEL TUBBENHAUER
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Campus Irchel, Office Y27J32, CH-8057Zürich, Switzerland, e-mail: daniel.tubbenhauer@math.uzh.ch
PAUL WEDRICH
Affiliation:
Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, CA94720, USA, e-mail: p.wedrich@gmail.com
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Abstract

In this note, we compute the centers of the categories of tilting modules for G = SL2 in prime characteristic, of tilting modules for the corresponding quantum group at a complex root of unity, and of projective GgT-modules when g = 1, 2.

MSC classification

Primary: 20G05: Representation theory 20C20: Modular representations and characters
Secondary: 17B10: Representations, algebraic theory (weights)

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 165 - 184
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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References

Andersen, H. H., Tilting modules and cellular categories, J. Pure Appl. Algebra 224(9) (2020), 106366. Available at doi: 10.1016/j.jpaa.2020.106366.CrossRefGoogle Scholar
Andersen, H. H., Stroppel, C. and Tubbenhauer, D., Cellular structures using U q -tilting modules, Pacific J. Math. 292(1) (2018), 21–59. Available at https://arxiv.org/abs/1503.00224, doi: 10.2140/pjm.2018.292.21.CrossRefGoogle Scholar
Andersen, H. H. and Tubbenhauer, D., Diagram categories for U q -tilting modules at roots of unity, Transform. Groups 22(1) (2017), 29–89. Available at https://arxiv.org/abs/1808.08022, doi: 10.1007/s00031-016-9363-z.CrossRefGoogle Scholar
Donkin, S., On tilting modules for algebraic groups, Math. Z. 212(1) (1993), 39–60. doi: 10.1007/BF02571640.CrossRefGoogle Scholar
Tubbenhauer, D. and Wedrich, P., Quivers for SL(2) tilting modules. Preprint. Available at https://arxiv.org/abs/1907.11560.Google Scholar
Williamson, G., Algebraic representations and constructible sheaves, Jpn. J. Math. 12(2) (2017), 211–259. Available at https://arxiv.org/abs/1610.06261, doi: 10.1007/s11537-017-1646-1.CrossRefGoogle Scholar