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Chapter 2 Thick calculus for the nilHecke ring. Chapter 3 Brief review of calculus for categorified sl2. Chapter 4 Thick calculus and.
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Facebook Twitter Pinterest Share. Description A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl 2 was constructed in a paper arXiv Here the authors enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions.
They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements. These formulas have integral coefficients and imply that one of the main results of Lauda's paper--identification of the Grothendieck ring of his 2-category with the idempotented quantum sl 2 --also holds when the 2-category is defined over the ring of integers rather than over a field.
Extended graphical calculus for categorified quantum sl(2)
A new diagrammatic description of Schur functions is also given and it is shown that the the Jacobi-Trudy formulas for the decomposition of Schur functions into elementary or complete symmetric functions follows from the diagrammatic relations for categorified quantum sl 2. Aaron D. Abstract Article info and citation First page References Abstract We show that Khovanov homology and its s l 3 variant can be understood in the context of higher representation theory. Article information Source Algebr.
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