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sl(2) actions on Soergel bimodules

Presenter
November 7, 2021
Abstract
Bott-Samelson bimodules are bimodules over a polynomial ring, whose summands are Soergel bimodules. In type A, they are commonly used in the definition of triply-graded knot homology. This polynomial ring admits an action of the lie algebra sl(2) by derivations, leading to an action on Bott-Samelson bimodules, and an action on morphisms between Bott-Samelson bimodules. The raising operator in sl(2) agrees with the differential used when equipping these categories with p-dg structures. A major open question is whether this leads to a consistent action of sl(2) on Soergel bimodules, as the idempotents used to project to these summands are not invariant under sl(2). If so, this has a number of interesting implications.
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