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Full-Text Articles in Physical Sciences and Mathematics
Mixed Categories, Formality For The Nilpotent Cone, And A Derived Springer Correspondence, Laura Joy Rider
Mixed Categories, Formality For The Nilpotent Cone, And A Derived Springer Correspondence, Laura Joy Rider
LSU Doctoral Dissertations
Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to an equivalence between the triangulated category generated by the Springer perverse sheaf and the derived category of di_x000B_erential graded modules over a dg-ring related to the Weyl group
Graham's Variety And Perverse Sheaves On The Nilpotent Cone, Amber Russell
Graham's Variety And Perverse Sheaves On The Nilpotent Cone, Amber Russell
LSU Doctoral Dissertations
In recent work, Graham has defined a variety which maps to the nilpotent cone, and which shares many properties with the Springer resolution. However, Graham's map is not an isomorphism over the principal orbit, and for type A in particular, its fibers have a nice relationship with the fundamental groups of the nilpotent orbits. The goal of this dissertation is to determine which simple perverse sheaves appear when the Decomposition Theorem for perverse sheaves is applied in Graham's setting for type A, and to begin to answer this question in the other types as well. In Chapter 1, we give …
Perverse Poisson Sheaves On The Nilpotent Cone, Jared Lee Culbertson
Perverse Poisson Sheaves On The Nilpotent Cone, Jared Lee Culbertson
LSU Doctoral Dissertations
For a reductive complex algebraic group, the associated nilpotent cone is the variety of nilpotent elements in the corresponding Lie algebra. Understanding the nilpotent cone is of central importance in representation theory. For example, the nilpotent cone plays a prominent role in classifying the representations of finite groups of Lie type. More recently, the nilpotent cone has been shown to have a close connection with the affine flag variety and this has been exploited in the Geometric Langlands Program. We make use of the following important fact. The nilpotent cone is invariant under the coadjoint action of G on the …