A categorification of the Beilinson-Lusztig-MacPherson type of the quantum sl(2) was once built in a paper (arXiv:0803.3652) through Aaron D. Lauda. right here the authors improve the graphical calculus brought and constructed in that paper to incorporate two-morphisms among divided powers one-morphisms and their compositions. They receive specific diagrammatical formulation for the decomposition of goods of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical foundation parts. those formulation have vital coefficients and suggest that one of many major result of Lauda's paper--identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)--also holds whilst the 2-category is outlined over the hoop of integers instead of over a box. a brand new diagrammatic description of Schur services is additionally given and it really is proven that the the Jacobi-Trudy formulation for the decomposition of Schur capabilities into straightforward or whole symmetric capabilities follows from the diagrammatic family for categorified quantum sl(2).
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