Alcove path model for $B(\infty )$

Abstract

We construct a model for $B(\infty )$ using the alcove path model of Lenart and Postnikov. We show that the continuous limit of our model recovers a dual version of the Littelmann path model for $B(\infty )$ given by Li and Zhang. Furthermore, we consider the dual version of the alcove path model and obtain analogous results for the dual model, where the continuous limit gives the Li and Zhang model.

19 pages, 7 figures; improvements from comments, added more figures

References in corpus (4)

• A rigged configuration model for $B(\infty )$
• Rigged configurations for all symmetrizable types
• Rigged configurations and the $\ast$-involution
• Connecting marginally large tableaux and rigged configurations via crystals

Cited by in corpus (1)

• A new description of the bicrystal $B(\infty )$ and the extended crystal