pseudorepresentation

English

Etymology

From pseudo- +‎ representation.

Noun

pseudorepresentation (plural pseudorepresentations)

1. (mathematics) Given a group $G$ and a commutative ring $R$, a tuple of maps $(a,d,x)$, where $a,d:G\to R$ and $x:GxG\to R$, are a pseudorepresentation if they satisfy the relations one would expect if $a(g)$ and $d(g)$ were the diagonal entries of a two dimensional representation $\begin{array}{c}|a(g)b(g)|\\ |c(g)d(g)|\end{array}$ and if $x$ was given by $x(g,g^{\prime })=b(g)c(g^{\prime })$.
   • 2015, Jyoti Prakash Saha, “Variation of Weyl modules in $p$-adic families”, in arXiv‎^[1]:

     More generally, we prove that the structures of the Frobenius-semisimplifications of the Weyl modules attached to a collection of pure representations are rigid if these pure representations lift to Weil-Deligne representations over domains containing $𝒪$ and the traces of these lifts are parametrized by a pseudorepresentation over $𝒪$..