Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2016

Author dc:creator

• Matherne, Jacob Paul

• Geometric Satake
• Springer correspondence
• small representations
• perverse sheaves
• algebraic groups

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-07022016-000813
https://repository.lsu.edu/gradschool_dissertations/668

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1667