Doctor of Philosophy (PhD)
It is known that the geometric Satake equivalence is intimately related to the Springer correspondence when restricting to small representations of the Langlands dual group (see a paper by Achar and Henderson and one by Achar, Henderson, and Riche). This dissertation relates the derived geometric Satake equivalence of Bezrukavnikov and Finkelberg and the derived Springer correspondence of Rider when we restrict to small representations of the Langlands dual group under consideration. The main theorem of the before-mentioned paper of Achar, Henderson, and Riche sits inside this derived relationship as its degree zero piece.
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Matherne, Jacob Paul, "Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations" (2016). LSU Doctoral Dissertations. 668.
Achar, Pramod N.