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Categorified sl_N spiders and Sym^n-projectors
Algebra & Discrete Mathematics| Speaker: | Matt Hogancamp, U Indiana |
| Location: | 1147 MSB |
| Start time: | Fri, Feb 19 2016, 1:10PM |
Description
The sl_N ``spider'' (a notion introduced by Greg Kuperberg) is a
diagrammatically defined category whose idempotent completion is
equivalent to the category of finite dimensional representations of sl_N
(or rather, the associated quantum group). Primitive idempotents in
the spider play the role of irreducuble representations. Of particular
importance are the ``generalized Jones-Wenzl projectors,'' which are
projections onto the symmetric powers of the fundamental representation.
In this expository talk I will describe a categorification of sl_N
spider, and I will discuss how the generalized Jones-Wenzl projectors
are categorified by certain infinite chain complexes. The categorified
projections posses a lot of interesting structure, and can be used to
defined colored link homology theories.
Note the special day /extra A&DM seminar this week. Hogancamp is in town Feb18-22.