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Transactions of the American Mathematical Society

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

 
 

 

Affine zigzag algebras and imaginary strata for KLR algebras


Authors: Alexander Kleshchev and Robert Muth
Journal: Trans. Amer. Math. Soc. 371 (2019), 4535-4583
MSC (2010): Primary 20C08, 17B10, 05E10
DOI: https://doi.org/10.1090/tran/7464
Published electronically: September 13, 2018
MathSciNet review: 3934461
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Abstract: KLR algebras of affine $\texttt {ADE}$ types are known to be properly stratified if the characteristic of the ground field is greater than some explicit bound. Understanding the strata of this stratification reduces to semicuspidal cases, which split into real and imaginary subcases. Real semicuspidal strata are well understood. We show that the smallest imaginary stratum is Morita equivalent to Huerfano-Khovanov’s zigzag algebra tensored with a polynomial algebra in one variable. We introduce affine zigzag algebras and prove that these are Morita equivalent to arbitrary imaginary strata if the characteristic of the ground field is greater than the bound mentioned above.


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Additional Information

Alexander Kleshchev
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
MR Author ID: 268538
Email: klesh@uoregon.edu

Robert Muth
Affiliation: Department of Mathematics, Washington and Jefferson College, Washington, Pennsylvania 15301
MR Author ID: 1191042
Email: rmuth@washjeff.edu

Received by editor(s): January 20, 2016
Received by editor(s) in revised form: June 19, 2017
Published electronically: September 13, 2018
Additional Notes: The first author was supported by the NSF grant DMS-1161094, Max-Planck-Institut, and the Fulbright Foundation.
Article copyright: © Copyright 2018 American Mathematical Society