PreprintCC BY 4.0arXiv
Hitchin's Conjecture for sln in Odd Prime Degree
Abstract
We prove Hitchin's conjecture for sln in every odd prime degree. More precisely, let p=2k+1 be prime and let n≥ k+1. Every nonzero primitive element α∈Λp(sln*)sln is nonzero on the top exterior power of the unique p-dimensional irreducible submodule of sln for the adjoint action of a principal sl2-subalgebra. The conjecture also holds for types Bℓ and Cℓ, with ℓ≥2, in every prime degree p=4r−1 with 1≤ r≤ℓ.
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BibTeX
@misc{jia2026hitchins,
title = {{Hitchin's Conjecture for $\mathfraksl_n$ in Odd Prime Degree}},
author = {Boming Jia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12118},
eprint = {2609.12118},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12118},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hitchin's Conjecture for sl_n in Odd Prime Degree
AU - Boming Jia
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12118
UR - https://arxiv.org/abs/2609.12118
AB - We prove Hitchin's conjecture for sl_n in every odd prime degree. More precisely, let p=2k+1 be prime and let n≥ k+1. Every nonzero primitive element α∈Λ^p(sl_n^*)^sl_n is nonzero on the top exterior power of the unique p-dimensional irreducible submodule of sl_n for the adjoint action of a principal sl_2-subalgebra. The conjecture also holds for types B_ℓ and C_ℓ, with ℓ≥2, in every prime degree p=4r−1 with 1≤ r≤ℓ.
ER -