pseudorepresentation

English[edit]

pseudorepresentation (plural pseudorepresentations)

(mathematics) Given a group $G$ $G$ and a commutative ring $R$ $R$ , a tuple of maps $(a,d,x)$ $(a,d,x)$ , where $a,d:G\rightarrow R$ $a,d:G\rightarrow R$ and $x:GxG\rightarrow R$ $x:GxG\rightarrow R$ , are a pseudorepresentation if they satisfy the relations one would expect if $a(g)$ $a(g)$ and $d(g)$ $d(g)$ were the diagonal entries of a two dimensional representation ${\begin{matrix}|a(g)b(g)|\\|c(g)d(g)|\end{matrix}}$ ${\begin{matrix}|a(g)b(g)|\\|c(g)d(g)|\end{matrix}}$ and if $x$ $x$ was given by $x(g,g^{\prime })=b(g)c(g^{\prime })$ $x(g,g^{\prime })=b(g)c(g^{\prime })$ .
- 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 ${\mathcal {O}}$ and the traces of these lifts are parametrized by a pseudorepresentation over ${\mathcal {O}}$ ..