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Article overview
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Realizing the symplectic group as a Galois group over the function field $mathbb{F}_q(t)$ | | Rod Gow
; Gary McGuire
; | | Date: |
2 Sep 2023 | | Abstract: | We realize the symplectic group $Sp(2m,q)$ as a Galois group over the
function field $mathbb{F}_q(t)$, where $q$ is a power of the prime $p$. Our
proof is based on the study of certain so-called $q$-palindromic polynomials,
whose roots form a vector space over $mathbb{F}_q$. The main thrust of our
approach is to find symplectic transvections in the Galois group and to exploit
the fact that the Galois group acts transitively on the nonzero roots in the
irreducible case. | | Source: | arXiv, 2309.00880 | | Services: | Forum | Review | PDF | Favorites | |
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