  We develop a diagrammatic categorification of the polynomial ring 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.

Representation Theory;Quantum Algebra