Pré-Publication, Document De Travail Année : 2023

SYMPLECTIC DETERMINANT LAWS AND INVARIANT THEORY

Résumé

We introduce the notion of $\textit{symplectic determinant laws}$ by analogy with Chenevier's definition of determinant laws. Symplectic determinant laws are a way to define pseudorepresentations for symplectic representations of algebras with involution over arbitrary $\mathbb{Z}[\frac{1}{2}]$-algebras. We prove that this notion satisfies the properties expected from a good theory of pseudorepresentations, and we compare it to Lafforgue's $\text{Sp}_{2d}$-pseudocharacters. In the process, we compute generators of the invariant algebras $A[M_d^m]^{G}$ and $A[G^m]^G$ over an arbitrary commutative ring $A$ when $G \in \{\text{Sp}_d, \mathrm O_d, \text{GSp}_d, \text{GO}_d\}$, generalizing results of Zubkov.
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Dates et versions

hal-04256596 , version 1 (24-10-2023)

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  • HAL Id : hal-04256596 , version 1

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Mohamed Moakher, Julian Quast. SYMPLECTIC DETERMINANT LAWS AND INVARIANT THEORY. 2023. ⟨hal-04256596⟩
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