Extended graphical calculus for categorified quantum sl(2)
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 v, 87 p. : ill ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1029.
Access
Available online

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QA3 .A57 NO.1029

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QA3 .A57 NO.1029
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Contributors
 Contributor
 Khovanov, Mikhail.
Contents/Summary
 Publisher's Summary
 A categorification of the BeilinsonLusztigMacPherson form of the quantum sl(2) was constructed in a paper (arXiv:0803.3652) by Aaron D. Lauda. Here the authors enhance the graphical calculus introduced and developed in that paper to include twomorphisms between divided powers onemorphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers onemorphisms as direct sums of indecomposable onemorphisms; 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 paperidentification of the Grothendieck ring of his 2category with the idempotented quantum sl(2)also holds when the 2category is defined over the ring of integers rather than over a field. A new diagrammatic description of Schur functions is also given and it is shown that the the JacobiTrudy formulas for the decomposition of Schur functions into elementary or complete symmetric functions follows from the diagrammatic relations for categorified quantum sl(2).
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2012
 Responsibility
 Mikhail Khovanov ... [et al.].
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1029
 Note
 "September 2012, volume 219, number 1029 (second of 5 numbers)."
 ISBN
 9780821889770
 082188977X