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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. Path combinatorics and light leaves for quiver Hecke algebras. Mathematische Zeitschrift,

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.

Publication Type: Article
Additional Information: arXiv admin note: text overlap with arXiv:2005.02825
Publisher Keywords: math.RT; math.RT; math.CO
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 30 Oct 2020 13:59
URI: https://openaccess.city.ac.uk/id/eprint/25146
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