Ext enhanced Soergel bimodules, link homology, and Gomi's trace

Abstract: Soergel Bimodules began as an alternative approach to proving the illustrious Kazhdan-Lusztig conjectures and have since become a cornerstone of representation theory and link homology. In this talk, we will give a diagrammatic presentation for Ext groups between Soergel Bimodules in rank 2 à la Elias-Khovanov and Elias-Williamson. We then use our results to (1) show how it helps with computing triply graded link homology for braids on 3 strands (2) show how Ext groups of Soergel Bimodules in rank 2 categorifies Gomi's Trace, a generalization of Markov's trace to the Hecke algebra of any finite Coxeter group.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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