Diagrammatic categorification of the Chebyshev polynomials of the second kind. (English) Zbl 1480.16037
Summary: We develop a diagrammatic categorification of the polynomial ring \((\mathbb Z[x]\), based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead to the first topological interpretations of the Bernstein-Gelfand-Gelfand reciprocity property.
MSC:
| 16G99 | Representation theory of associative rings and algebras |
| 16S99 | Associative rings and algebras arising under various constructions |
| 18G10 | Resolutions; derived functors (category-theoretic aspects) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
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