PreprintCC BY 4.0arXiv
On the elliptic Hall category
Abstract
In this paper we study (the positive half of) the elliptic Hall category, a categorical version of the elliptic Hall algebra. Our main result is a computation of categorical versions of the generators in the coherent realization of the elliptic Hall category, i.e., via coherent sheaves on commuting stacks for GLn× gln: we realize them as Hodge associated graded sheaves of certain twisted equivariant D-modules on the groups GLn.
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BibTeX
@misc{bezrukavnikov2026elliptic,
title = {{On the elliptic Hall category}},
author = {Roman Bezrukavnikov and Ivan Losev and Xinchun Ma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33992},
eprint = {2610.33992},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33992},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the elliptic Hall category
AU - Roman Bezrukavnikov
AU - Ivan Losev
AU - Xinchun Ma
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.33992
UR - https://arxiv.org/abs/2610.33992
AB - In this paper we study (the positive half of) the elliptic Hall category, a categorical version of the elliptic Hall algebra. Our main result is a computation of categorical versions of the generators in the coherent realization of the elliptic Hall category, i.e., via coherent sheaves on commuting stacks for GL_n× gl_n: we realize them as Hodge associated graded sheaves of certain twisted equivariant D-modules on the groups GL_n.
ER -