Computational complexity of immanents and representations of the full linear group

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Determinantal Point Processes for Machine Learning (2012, background): “Complexity results for immanants are less definitive, with certain classes of immanants apparently hard to compute [19, 20], while some upper bounds on complexity are known [5, 65], and at least one nontrivial case is efficiently computable [62].”
The Computational Complexity of Immanants (2000, background): “This upper bound improves previous bounds due to Hartmann [11] and Barvinok [1].”