Year: 2026
Type: preprint
Abstract: We prove Hitchin's conjecture for $\mathfrak{sl}_n$ in every odd prime degree. More precisely, let $p=2k+1$ be prime and let $n\geq k+1$. Every nonzero primitive element $α\inΛ^p(\mathfrak{sl}_n^*)^{\mathfrak{sl}_n}$ is nonzero on the top exterior power of the unique $p$-dimensional irreducible submodule of $\mathfrak{sl}_n$ for the adjoint action of a principal $\mathfrak{sl}_2$-subalgebra. The conjecture also holds for types $B_\ell$ and $C_\ell$, with $\ell\geq2$, in every prime degree $p=4r-1$ with $1\leq r\leq\ell$.
Source: arXiv (Cornell University)
Author: Jia, Boming
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7785972365
OpenAlex ID: W7212503306