Extended Graphical Calculus for Categorified Quantum Sl2 - Brossura

Khovanov, Mikhail; Lauda, Aaron D.; Mackaay, Marco; Stosic, Marko

Brossura

ISBN 10: 082188977X ISBN 13: 9780821889770

Casa editrice: Amer Mathematical Society, 2012

Riassunto

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).

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 082188977X
• ISBN 13: 9780821889770
• Rilegatura: Copertina flessibile
• Numero di pagine: 87
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile