Extremal weight projectors II

Abstract

In previous work, we have constructed diagrammatic idempotents in an affine extension of the Temperley-Lieb category, which describe extremal weight projectors for sl(2), and which categorify Chebyshev polynomials of the first kind. In this paper, we generalize the construction of extremal weight projectors to the case of gl(N) for N greater than or equal to 2, with a view towards categorifying the corresponding torus skein algebras via Khovanov-Rozansky link homology. As by-products, we obtain compatible diagrammatic presentations of the representation categories of gl(N) and its Cartan subalgebra, and a categorification of power-sum symmetric polynomials.

arXiv comment32 pages

References in corpus (9)

• Khovanov's homology for tangles and cobordisms
• Spiders for rank 2 Lie algebras
• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• A positive basis for surface skein algebras
• Super $q$-Howe duality and web categories
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• Quantum K-theoretic geometric Satake
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Cited by in corpus (4)

• A Generalization of the Gram determinant of type A
• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
• gl(2) foams and the Khovanov homotopy type
• A graphical categorification of the two-variable Chebyshev polynomials of the second kind