Journal article

Combinatorics in affine flag varieties

James Parkinson, Arun Ram, Christoph Schwer

JOURNAL OF ALGEBRA | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2009

Abstract

The Littelmann path model gives a realization of the crystals of integrable representations of symmetrizable Kac-Moody Lie algebras. Recent work of Gaussent and Littelmann [S. Gaussent, P. Littelmann, LS galleries, the path model, and MV cycles, Duke Math. J. 127 (1) (2005) 35-88] and others [A. Braverman, D. Gaitsgory, Crystals via the affine Grassmannian, Duke Math. J. 107 (3) (2001) 561-575; S. Gaussent, G. Rousseau, Kac-Moody groups, hovels and Littelmann's paths, preprint, arXiv: math.GR/0703639, 2007] has demonstrated a connection between this model and the geometry of the loop Grassmanian. The alcove walk model is a version of the path model which is intimately connected to the combin..

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University of Melbourne Researchers