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Diagrammatics of Folded Soergel Bimodules of type A1xA1

Algebra & Discrete Mathematics

Speaker: Nicolas Jaramillo Torres, University of Oregon
Related Webpage:
Location: 2112 MSB
Start time: Tue, Nov 14 2023, 4:10PM

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.