Path combinatorics and light leaves for quiver Hecke algebras

TY - JOUR

T1 - Path combinatorics and light leaves for quiver Hecke algebras

AU - Bowman, Chris

AU - Cox, Anton

AU - Hazi, Amit

AU - Michailidis, Dimitris

N1 - 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).

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85115989819&partnerID=8YFLogxK

U2 - 10.1007/s00209-021-02829-0

DO - 10.1007/s00209-021-02829-0

M3 - Article

AN - SCOPUS:85115989819

SN - 0025-5874

VL - 300

SP - 2167

EP - 2203

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

ER -