Geodesic
Modified traces on Deligne's category $\underline{\mathrm{Re}}\mathrm p(S_t)$
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 4, pp. 541-560.

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Summary: Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne's category admits a unique nontrivial family of modified trace functions. Such modified trace functions have already proven to be interesting in both low-dimensional topology and representation theory. We also introduce a graded variant of Deligne's category, lift the modified trace functions to the graded setting, and use them to recover the well-known invariant of framed knots known as the writhe.
Keywords: ribbon category, Deligne's category, symmetric groups, modified traces 
@article{JAC_2012__36_4_a4,
     author = {Comes, Jonathan and Kujawa, Jonathan R.},
     title = {Modified traces on {Deligne's} category $\underline{\mathrm{Re}}\mathrm p(S_t)$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {541--560},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_4_a4/}
}
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Comes, Jonathan; Kujawa, Jonathan R. Modified traces on Deligne's category $\underline{\mathrm{Re}}\mathrm p(S_t)$. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 4, pp. 541-560. http://geodesic.mathdoc.fr/item/JAC_2012__36_4_a4/