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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 & Michailidis, D. (2022). Path combinatorics and light leaves for quiver Hecke algebras. Mathematische Zeitschrift, 300, pp. 2167-2203. 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
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Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology
Text - Published Version
Available under License Creative Commons Attribution.

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