pseudorepresentation

From pseudo- +‎ representation.

pseudorepresentation (plural pseudorepresentations)

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

     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 ${\displaystyle {\mathcal {O}}}$ and the traces of these lifts are parametrized by a pseudorepresentation over ${\displaystyle {\mathcal {O}}}$..