PreprintCC BY-NC-ND 4.0arXiv
The coherent KLR sheaf
Abstract
We construct the KLR algebra (in type A) as affine sections of a coherent sheaf ℰ on a product of projective spaces ℙn. It was shown by Elias-Qi that the Lie algebra sl2 acts on such KLR algebras; our construction geometrically explains this action as stemming from the sl2-action on the twisting sheaves 𝒪(k) of ℙ1 and gives the maximal finite-dimensional sl2-submodule of KLR as global sections of ℰ. We furthermore extend the Elias-Qi action to a Witt action. Kleshchev-Loubert-Miemietz showed that the KLR of type A has a graded affine cellular structure; our construction also gives a geometric incarnation of this.
Related
- Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf
- The Chern character of a coherent sheaf on a smooth projective hypersurface
- Moduli descriptions of v-sheaf local models
- Bridging Denotator Theory and Sheaf Neural Networks for Symbolic Music Generation
- Non-vanishing of the structure-sheaf cohomology of affine henselian schemes and henselian affinoids
BibTeX
@misc{haseliu2026coherent,
title = {{The coherent KLR sheaf}},
author = {Matthew Hase-Liu and Fan Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15954},
eprint = {2609.15954},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15954},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The coherent KLR sheaf
AU - Matthew Hase-Liu
AU - Fan Zhou
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15954
UR - https://arxiv.org/abs/2609.15954
AB - We construct the KLR algebra (in type A) as affine sections of a coherent sheaf ℰ on a product of projective spaces ℙ^n. It was shown by Elias-Qi that the Lie algebra sl_2 acts on such KLR algebras; our construction geometrically explains this action as stemming from the sl_2-action on the twisting sheaves 𝒪(k) of ℙ^1 and gives the maximal finite-dimensional sl_2-submodule of KLR as global sections of ℰ. We furthermore extend the Elias-Qi action to a Witt action. Kleshchev-Loubert-Miemietz showed that the KLR of type A has a graded affine cellular structure; our construction also gives a geometric incarnation of this.
ER -