Categorification of the polynomial ring Z[x]
Radmila Sazdanovic (University of Pennsylvania)
Abstract:
We develop a diagrammatic categorification of the polynomial ring Z[x], based on the geometrically defined graded algebra and show how to lift various operations on polynomials to the categorified setting. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to x^n and standard modules to (x-1)^n in the Grothendieck ring. This construction generalizes to categorification of various orthogonal polynomials, including Chebyshev polynomials and the Hermite polynomials.