Physical Sciences and Mathematics Commons^™

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 …