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Creators/Authors contains: "Elias, Ben"

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  1. ; (, Duke Mathematical Journal)
    We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced in an earlier paper of the authors. We prove our conjecture in type A, and as a result we obtain a categorification of the Young idempotents. 
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  2. ; ; ; (, Duke Mathematical Journal)
    We introduce the notion of a categorical valuative invariant of polyhedra or matroids, in which alternating sums of numerical invariants are replaced by split exact sequences in an additive category. We provide categorical lifts of a number of valuative invariants of matroids, including the Poincar ́e polynomial, the Chow and augmented Chow polynomials, and certain two-variable extensions of the Kazhdan–Lusztig polynomial and Z-polynomial. These lifts allow us to perform calculations equivariantly with respect to automorphism groups of matroids. 
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  3. ; (, Annales mathématiques Blaise Pascal)
    We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules. 
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  4. ; (, Compositio Mathematica)
    null (Ed.)
    We introduce a new method for computing triply graded link homology, which is particularly well adapted to torus links. Our main application is to the $(n,n)$ -torus links, for which we give an exact answer for all $$n$$ . In several cases, our computations verify conjectures of Gorsky et al. relating homology of torus links with Hilbert schemes. 
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