2020/09/03 by C. Bowman, Bowman, C., Anton Cox +5
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2009.01705
openalex publication_date 2020/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.