An analogue of Jeu de taquin for Littelmann's crystal paths.
Year: 1998
Type: article
Abstract: Littelmann has given a combinatorial model for the characters of representations of semisimple Lie algebras, in terms of certain paths traced in the space of (rational) weights. From it, a description of the decomposition of tensor products can be derived that generalises the Littlewood-Richardson rule (the latter is valid in type An only). We present a new combinatorial construction that expresses in a bijective manner the symmetry of the tensor product in this path model. In type An , where there is a correspondence between paths and skew tableaux, this construction is equivalent to Schutzenberger's jeu de taquin; in the general case the construction retains its most crucial properties of symmetry and confluence. 1991 Mathematics Subject Classification: 05E10. Keywords and Phrases: Jeu de taquin, Littlewood-Richardson rule, crystal graphs, path crystals. 1 1 Introduction x1. Introduction. In this note we wish to present a simple construction that appears to arise natu...
Authors: van Leeuwen, Marc Armbruester
Institution: Université de Poitiers
Language: French
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1589967386