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Trihedral Soergel bimodules
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Resumo(s)
The quantum Satake correspondence relates dihedral Soergel bimodules to the
semisimple quotient of the quantum $\mathfrak{sl}_2$ representation category.
It also establishes a precise relation between the simple transitive
$2$-representations of both monoidal categories, which are indexed by bicolored
$\mathsf{ADE}$ Dynkin diagrams.
Using the quantum Satake correspondence between affine $\mathsf{A}_{2}$
Soergel bimodules and the semisimple quotient of the quantum $\mathfrak{sl}_3$
representation category, we introduce trihedral Hecke algebras and Soergel
bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These
have their own Kazhdan-Lusztig combinatorics, simple transitive
$2$-representations corresponding to tricolored generalized $\mathsf{ADE}$
Dynkin diagrams.
Descrição
Palavras-chave
2-representation theory Quantum groups and their fusion categories Hecke algebras Soergel bimodules Zigzag algebras