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Path combinatorics and light leaves for quiver Hecke algebras

Bowman, C., Cox, A. ORCID: 0000-0001-9799-3122, Hazi, A. ORCID: 0000-0001-7264-2211 and Michailidis, D. (2021). Path combinatorics and light leaves for quiver Hecke algebras. Mathematische Zeitschrift, doi: 10.1007/s00209-021-02829-0


We recast the classical notion of “standard tableaux" in an alcove-geometric setting and extend these classical ideas to all “reduced paths" in our geometry. This broader path-perspective is essential for implementing the higher categorical ideas of Elias–Williamson in the setting of quiver Hecke algebras. Our first main result is the construction of light leaves bases of quiver Hecke algebras. These bases are richer and encode more structural information than their classical counterparts, even in the case of the symmetric groups. Our second main result provides path-theoretic generators for the “Bott–Samelson truncation" of the quiver Hecke algebra.

Publication Type: Article
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering
Project Input:
Project IDFunder NameFunder ID
EP/V00090X/1Engineering and Physical Sciences Research Council
UNSPECIFIEDRoyal Commission for the Exhibition of 1851
Date available in CRO: 29 Sep 2021 15:16
Date deposited: 29 September 2021
Date of acceptance: 26 June 2021
Date of first online publication: 29 September 2021
Text - Published Version
Available under License Creative Commons Attribution.

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