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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Webs and $ q$-Howe dualities in types $ \mathbf{BCD}$


Authors: Antonio Sartori and Daniel Tubbenhauer
Journal: Trans. Amer. Math. Soc. 371 (2019), 7387-7431
MSC (2010): Primary 17B37, 17B10, 17B20; Secondary 20G42, 81R50
DOI: https://doi.org/10.1090/tran/7583
Published electronically: October 22, 2018
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Abstract: We define web categories describing intertwiners for the orthogonal and symplectic Lie algebras and, in the quantized setup, for certain orthogonal and symplectic coideal subalgebras. They generalize the Brauer category and allow us to prove quantum versions of some classical type $ \mathbf {BCD}$ Howe dualities.


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Additional Information

Antonio Sartori
Affiliation: Mathematisches Institut, Albert–Ludwigs-Universität Freiburg, Eckerstra$ß$e 1, 79104 Freiburg im Breisgau, Germany
Email: anton.sartori@gmail.com

Daniel Tubbenhauer
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Campus Irchel, Office Y27J32, CH-8057 Zürich, Switzerland
Email: daniel.tubbenhauer@math.uzh.ch

DOI: https://doi.org/10.1090/tran/7583
Keywords: Diagrammatic presentation, webs, (quantum) Brauer algebras, (quantum) Howe duality, classical Lie type, coideal subalgebras
Received by editor(s): January 12, 2017
Received by editor(s) in revised form: January 10, 2018, and March 21, 2018
Published electronically: October 22, 2018
Article copyright: © Copyright 2018 American Mathematical Society