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Publication
Two-color Soergel Calculus and Simple transitive 2-representations
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Advisor(s)
Abstract(s)
In this paper we complete the ADE-like classification of simple transitive
2-representations of Soergel bimodules in finite dihedral type, under the assumption of
gradeability. In particular, we use bipartite graphs and zigzag algebras of ADE type to give
an explicit construction of a graded (non-strict) version of all these 2-representations.
Moreover, we give simple combinatorial criteria for when two such 2-representations are
equivalent and for when their Grothendieck groups give rise to isomorphic representations.
Finally, our construction also gives a large class of simple transitive 2-representations in
infinite dihedral type for general bipartite graphs.
Description
Keywords
2-representation theory Zigzag algebra Soergel bimodule Hecke algebras for dihedral groups Categorification Kazhdan-Lusztig theory
