PreprintCC BY-SA 4.0arXiv
Decomposing the Action of Macdonald Operators for Classical Types
Abstract
We study Macdonald operators associated to classical root systems of types BN, CN, and DN. We provide explicit formulas for decomposing the cumulative action of these operators as the sum of the actions of lower-rank operators and auxiliary operators. We also discuss the same idea in the elliptic case, also known as Ruijsenaars operators, and show that under the trigonometric limit, the identity reduces to type-AN decomposition.
Related
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BibTeX
@misc{vu2026decomposing,
title = {{Decomposing the Action of Macdonald Operators for Classical Types}},
author = {Hieu Trung Vu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26389},
eprint = {2610.26389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26389},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Decomposing the Action of Macdonald Operators for Classical Types
AU - Hieu Trung Vu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26389
UR - https://arxiv.org/abs/2610.26389
AB - We study Macdonald operators associated to classical root systems of types B_N, C_N, and D_N. We provide explicit formulas for decomposing the cumulative action of these operators as the sum of the actions of lower-rank operators and auxiliary operators. We also discuss the same idea in the elliptic case, also known as Ruijsenaars operators, and show that under the trigonometric limit, the identity reduces to type-A_N decomposition.
ER -