A new diagrammatic 2-category models induction and restriction on Temperley-Lieb modules, with a basis theorem implying an equivalence after Karoubi completion and a positive basis from homogenized Chebyshev polynomials.
On the definition of Heisenberg category
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abstract
We revisit the definition of the Heisenberg category of central charge k. For central charge -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. For other negative central charges, the definition is due to Mackaay and Savage, also with some redundant relations, while central charge zero recovers the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.
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A Graphical Calculus for Induction and Restriction on Temperley-Lieb Modules
A new diagrammatic 2-category models induction and restriction on Temperley-Lieb modules, with a basis theorem implying an equivalence after Karoubi completion and a positive basis from homogenized Chebyshev polynomials.