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arXiv · 2206.01551

Linearized Polynomials, Galois Groups and Symmetric Power Modules

Rod Gow·Gary McGuire
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Abstract

We investigate some Galois groups of linearized polynomials over fields such as $\mathbb{F}_q(t)$. The space of roots of such a polynomial is a module for its Galois group. We present a realization of the symmetric powers of this module, as a subspace of the splitting field of another linearized polynomial.

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Rod Gow, Gary McGuire. 2022-06-03. Linearized Polynomials, Galois Groups and Symmetric Power Modules. https://arxiv.org/abs/2206.01551

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