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Diagrammatics of Folded Soergel Bimodules of type A1xA1
Algebra & Discrete Mathematics| Speaker: | Nicolas Jaramillo Torres, University of Oregon |
| Related Webpage: | https://cas.uoregon.edu/directory/mathematics/all/nicolasj |
| Location: | 2112 MSB |
| Start time: | Tue, Nov 14 2023, 4:10PM |
Description
In this talk we show a
diagrammatic presentation for the equivariantization (or 'folding') of
the category of Soergel Bimodules of type A1xA1. Even though this is the
smallest case of folding, we were surprised to find
out there are a lot more relations than we expected.
The Grothendieck ring of this
category is a 5-dimensional algebra that specializes both to the
invariants of the Hecke algebra and to the Hecke algebra with unequal
parameters.
We will also show our future approaches to the subject: getting a light leaves basis and categorically diagonalize the full twist in this category.