Calogero-Moser Polynomial Approximations and Dwork Congruences for Complete Flags
Abstract
We construct p-adic polynomial approximations to the zero-framing cohomological quasimap vertex of cotangent bundles to complete flag varieties from the trigonometric Calogero--Moser system. Negative integer couplings give regular staircase Jack polynomials with nonnegative integer coefficients. We compare them with complete-flag master polynomials extending the construction of Smirnov--Varchenko. Both families converge coefficientwise to the vertex and satisfy the full commuting equations modulo ps. For n≥3, we prove sharp degree-dependent congruences and compute leading residues at every p-power scale. Their discrepancy has coefficient norm p−1 and an exact weighted Gauss norm giving uniform decay on smaller closed polydiscs. For the master family, multivariable Dwork congruences reconstruct the vertex by an infinite product. The results hold in every rank for 0<r/d≤1/2 and odd prime p.
Related
- Dispersive decay and scattering for continuum Calogero--Moser models
- Well--posedness for the continuum Calogero--Moser equations by parabolic regularization
- Equivalence of superintegrable Poisson projection chains: magnetic cotangent bundles and spin Calogero-Moser models
- Stratified Superintegrability of Spin Calogero-Moser-Sutherland Systems
- Uniform-in-Time Approximation of Calogero-Moser Particles by Continuum Multisolitons
BibTeX
@misc{koroteev2026calogeromoser,
title = {{Calogero-Moser Polynomial Approximations and Dwork Congruences for Complete Flags}},
author = {Peter Koroteev},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02417},
eprint = {2611.02417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02417},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Calogero-Moser Polynomial Approximations and Dwork Congruences for Complete Flags
AU - Peter Koroteev
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02417
UR - https://arxiv.org/abs/2611.02417
AB - We construct p-adic polynomial approximations to the zero-framing cohomological quasimap vertex of cotangent bundles to complete flag varieties from the trigonometric Calogero--Moser system. Negative integer couplings give regular staircase Jack polynomials with nonnegative integer coefficients. We compare them with complete-flag master polynomials extending the construction of Smirnov--Varchenko. Both families converge coefficientwise to the vertex and satisfy the full commuting equations modulo p^s. For n≥3, we prove sharp degree-dependent congruences and compute leading residues at every p-power scale. Their discrepancy has coefficient norm p^−1 and an exact weighted Gauss norm giving uniform decay on smaller closed polydiscs. For the master family, multivariable Dwork congruences reconstruct the vertex by an infinite product. The results hold in every rank for 0<r/d≤1/2 and odd prime p.
ER -