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      Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory

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          Abstract

          We explain an elementary, topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group action and the component group action admit a diagrammatic description in terms of cup diagrams appearing in the context of Khovanov arc algebras of types B and D. We determine the decomposition of the representations into irreducibles and relate our construction to classical Springer theory. In addition to that we give a presentation of the cohomology ring of the two-block Springer fibers in types C and D.

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          Representations of Coxeter groups and Hecke algebras

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            Trigonometric sums, green functions of finite groups and representations of Weyl groups

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              A construction of representations of Weyl groups

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                Author and article information

                Journal
                2016-11-29
                Article
                1611.09828
                89fb85a5-44eb-4a11-921d-6413530aae6b

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                28 pages, comments welcome
                math.RT math.GT math.QA

                Geometry & Topology,Algebra
                Geometry & Topology, Algebra

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