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.
Heisenberg algebra and a graphical calculus
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abstract
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of vector spaces of morphisms between products of generating objects in this category.
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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.