Extended Graphical Calculus for Categorified Quantum Sl2 - Couverture souple

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

Couverture souple

ISBN 10 : 082188977X ISBN 13 : 9780821889770

Editeur : American Mathematical Society, 2012

Synopsis

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).

A propos du livre

À propos de l?auteur

Mikhail Khovanov is at Columbia University, New York, USA.

||Aaron D. Lauda is at University of Southern California, USA.

|Marco Mackaay is at Universidade do Algarve, Portugal.

|Marko Stosic is at Instituto Superior Tecnico, Portugal.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 082188977X
• ISBN 13: 9780821889770
• Reliure: Broché
• Nombre de pages: 87
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible