Power operations and central maps in representation theory
Name
1051190363-MIT.pdf
Description
Full printable version
Size
7.33 MB
Format
Adobe PDF
Checksum (MD5)
f00a2bd7578d968e84d1b92f96eed1df
Author(s)
Lonergan, Gus (Gus C.)
Advisor(s)
Roman Bezrukavnikov.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
The theme of this thesis is the novel application of techniques of algebraic topology (specifically, Steenrod's operations and Smith's localization theory) to representation theory (especially in the context of the geometric Satake equivalence). In Chapter 2, we use Steenrod's construction to prove that the quantum Coulomb branch is a Frobenius-constant quantization. We also demonstrate the corresponding result for the K-theoretic version of the quantum Coulomb branch. In Chapter 3, we develop the theory of parity sheaves with coefficients in the Tate spectrum, and use it to give a geometric construction of the Frobenius-contraction functor. In Chapter 4, we discuss some related results, including a geometric construction of the Frobenius twist functor, and also discuss future directions of research. The content of Chapter 3 is joint work with S. Leslie.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 153-155).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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