University of Cambridge > > Isaac Newton Institute Seminar Series > Categorical diagonalization

Categorical diagonalization

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact INI IT.

HTLW04 - Quantum topology and categorified representation theory

It goes without saying that diagonalization is an important tool in linear algebra and representation theory.  In this talk I will discuss joint work with Ben Elias in which we develop a theory of diagonalization of functors, which has relevance both to higher representation theory and to categorified quantum invariants.  For most of the talk I will use small examples to illustrate of components of the theory, as well as subtleties which are not visible on the linear algebra level.  I will also state our Diagonalization Theorem which, informally, asserts that an object in a monoidal category is diagonalizable if it has enough ``eigenmaps''.  Time allowing, I will also mention our main application, which is a diagonalization of the full-twist Rouquier complexes acting on Soergel bimodules in type A.  The resulting categorical eigenprojections categorify q-deformed Young idempotents in Hecke algebras, and are also important for constructing colored link homology theories which, conjecturally, are functorial under 4-d cobordisms.  

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2022, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity