There is no particular order to the items below. Caveat lector: A lot of these notes reflect my initial attempts at understanding a particular topic, much of the writing is quite bad, riddled with errors and incomplete.
The degenerate affine braid group and Schur-Weyl type duality
Monoidal categories [.pdf]
Some very incomplete and unpolished notes on monoidal categories and quantum groups. I don't expect there to be a cleaned up version of these this year, perhaps next year.
Jordan decompositon and Cartan's criterion [.pdf]
Toy example: 2x2 upper triangular matrices [.pdf]
Some computations about the representations of this algebra (or equivalently the representations of the quiver ●->●). This is a scan of handwritten notes.
Hopf algebras [.pdf]
The main goal of this note was to prove that a bijective antipode is automatically an algebra and coalgebra antiautomorphism. There are some representation theory tidbits in there too.
The determinant [.pdf]
This is a scan of handwritten notes.
The BGG category O: definition [.pdf]
I wrote these a long time ago (rediscovered during hard drive spring cleaning). As such the writing is worse than usual.
Derived categories and perverse sheaves: Lecture I [.pdf], Lecture II [.pdf], Lecture III [.pdf], Lecture IV [.pdf], Lecture V [.pdf]
These are scans of my notes on Pramod Achar's lectures during the Algebraic Lie Theory Instructional Workshop at the Newton Institute in January 2009.
Symmetry, polynomials and quantization: Lecture I [.pdf], Lecture II [.pdf], Lecture III [.pdf], Lecture IV [.pdf]
These are scans of my notes on Arun Ram's lectures during the Algebraic Lie Theory Instructional Workshop at the Newton Institute in January 2009.
sl2-categorification and derived equivalences: Lecture I [.pdf], Lecture II [.pdf], Lecture III [.pdf]
These are scans of my notes on Joe Chuang's lectures during the Algebraic Lie Theory Instructional Workshop at the Newton Institute in January 2009.
Higher representations of Lie algebras: Lecture I [.pdf], Lecture II [.pdf], Lecture III [.pdf], Lecture IV [.pdf], Lecture V [.pdf]
These are scans of my notes on Raphael Rouquiër's lectures during the Algebraic Lie Theory Instructional Workshop at the Newton Institute in January 2009.
Representations of real reductive groups: Lecture I [.pdf], Lecture II [.pdf], Lecture III [.pdf], Lecture IV [.pdf]
These are scans of my note on David Vogan's lectures during the Algebraic Lie Theory Instructional Workshop at the Newton Institute in January 2009.
Triangulated functor categories [.pdf]
The title should be interpreted as `categories of functors that have a triangulated structure on them'. These are notes on a framework/formalism for adjoint functors and derived equivalences that I have been developing as groundwork for what will one day (hopefully) be a PhD thesis.
Generation and equivalences in abelian and triangulated categories [.pdf]
This note is related to (and in many ways superceded by) the previous note on triangulated functor categories.
The Octahedron axiom [.pdf]
This is a brief note on some of the redundancy in the axioms for a triangulated category (I believe this observation is originally due to J.P. May). The note is primarily an excuse/exercise to develop some comfort with using the octahedron axiom.
Graph homology [.pdf]
This is a scan of handwritten notes.
Long exact sequence of cohomology [.pdf]
The one proof that every book on homological algebra leaves as an exercise: constructing the connnecting map. These are scans of handwritten notes.
Last updated: 27 September, 2009