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Categorification of the genus two DAHA
Abstract
We construct three derived endofunctors on the derived category of graded integrable representations of the current algebra of a flat degeneration of D(2|1,α), and prove that their classes in the Grothendieck group are the genus two Macdonald operators. Computing the graded Ext pairing explicitly, we deduce the self-adjointness of the genus two Macdonald operators and the orthogonality of genus $2$ Macdonald polynomials with respect to the certain skew-bilinear form.
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BibTeX
@misc{arthamonov2026categorification,
title = {{Categorification of the genus two DAHA}},
author = {Semeon Arthamonov and Ievgen Makedonskyi and Daniil Sarafannikov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.13278},
eprint = {2608.13278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13278},
}
RIS
TY - UNPB
TI - Categorification of the genus two DAHA
AU - Semeon Arthamonov
AU - Ievgen Makedonskyi
AU - Daniil Sarafannikov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2608.13278
UR - https://arxiv.org/abs/2608.13278
AB - We construct three derived endofunctors on the derived category of graded integrable representations of the current algebra of a flat degeneration of D(2|1,α), and prove that their classes in the Grothendieck group are the genus two Macdonald operators. Computing the graded Ext pairing explicitly, we deduce the self-adjointness of the genus two Macdonald operators and the orthogonality of genus $2$ Macdonald polynomials with respect to the certain skew-bilinear form.
ER -