Path combinatorics and light leaves for quiver Hecke algebras

Abstract

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.

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Item Type:	Article
Authors/Creators:	Bowman, Chris https://orcid.org/0000-0001-6046-8930 Cox, Anton Hazi, Amit Michailidis, Dimitris
Copyright, Publisher and Additional Information:	Funding Information: The first and third authors thank the Institut Henri Poincaré for hosting us during the thematic trimester on representation theory. The first author was funded by EPSRC grant EP/V00090X/1 and the third author was funded by the Royal Commission for the Exhibition of 1851. The authors would like to express their gratitude to the referee for their incredibly helpful comments and careful reading of the paper. Funding Information: The first and third authors thank the Institut Henri Poincar? for hosting us during the thematic trimester on representation theory. The first author was funded by EPSRC grant EP/V00090X/1 and the third author was funded by the Royal Commission for the Exhibition of 1851. The authors would like to express their gratitude to the referee for their incredibly helpful comments and careful reading of the paper. Publisher Copyright: © 2021, The Author(s).
Dates:	Published: March 2022 Published (online): 29 September 2021 Accepted: 26 June 2021
Institution:	The University of York
Academic Units:	The University of York > Faculty of Sciences (York) > Mathematics (York)
Funding Information:	Funder Grant number EPSRC EP/V00090X/1
Depositing User:	Pure (York)
Date Deposited:	01 Jul 2021 10:50
Last Modified:	19 Nov 2024 00:40
Published Version:	https://doi.org/10.1007/s00209-021-02829-0
Status:	Published
Refereed:	Yes
Identification Number:	10.1007/s00209-021-02829-0
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/pdf/2009.01705.pdf
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:175791

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Path combinatorics and light leaves for quiver Hecke algebras

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