pseudorepresentation
nounEtymology From pseudo- + representation.
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Mathematics, Sciences Given a group G and a commutative ring R, a tuple of maps (a,d,x), where a,d:G→R and x:GxG→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 |a(g)b(g)|\|c(g)d(g)| and if x was given by x(g,g^′)=b(g)c(g^′).
- 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 #92;mathcal#123;O#125; and the traces of these lifts are parametrized by a pseudorepresentation over #92;mathcal#123;O#125;..2015, Jyoti Prakash Saha, “Variation of Weyl modules in p-adic families”, in arXiv: