Extended graphical calculus for categorified quantum sl(2)
- Providence, R.I. : American Mathematical Society, c2012.
- Physical description
- v, 87 p. : ill ; 26 cm.
- Memoirs of the American Mathematical Society ; no. 1029.
QA3 .A57 NO.1029
- Unknown QA3 .A57 NO.1029
- Khovanov, Mikhail.
- Publisher's Summary
- A categorification of the Beilinson-Lusztig-MacPherson 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 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. 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).
(source: Nielsen Book Data)
- Publication date
- Mikhail Khovanov ... [et al.].
- Memoirs of the American Mathematical Society, 0065-9266 ; no. 1029
- "September 2012, volume 219, number 1029 (second of 5 numbers)."