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Showing 1 to 6 of 6 for “"Braid group action"”.
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Knot Floer Homology and Categorification
… of twisted Soergel bimodules and construct a braid group action on the homotopy category of complexes of twisted Soergel bimodules. We prove that the category of twisted Soergel bimodules categorifies the Hecke algebra with an extra indeterminate and its inverse adjoined. The braid group …
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Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras
… the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the …
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra
… classes associated to Bezrukavnikov–Riche’s braid group action for the Springer resolution. In particular, we obtain that the coherent Springer sheaf lies in cohomological degree 0 (i.e., is a sheaf rather than a complex), resolving a conjecture of Ben-Zvi–Chen–Helm–Nadler and Zhu. As a …
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Coherent sheaves on varieties arising in Springer theory, and category 0
… weights for an arbitrary simple algebraic group H, and 0, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit (as originally conjectured by Lusztig and Vogan). Here we prove an analogous statement for the …
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Quantum Toroidal Superalgebras
… that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed. The superalgebra E(s) contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂(m|n) with parity "s", called vertical and horizontal subalgebras. We show the …
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Kazhdan-Laumon Categories and Representations
… an abelian category A associated to a reductive group G over a finite field, with the aim of using it to construct discrete series representations of the finite Chevalley group G(F subscript q). The welldefinedness of their construction depended on their conjecture that this category has finite …