Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 029, 12 pages      math.CO/0610719      http://dx.doi.org/10.3842/SIGMA.2007.029
Contribution to the Vadim Kuznetsov Memorial Issue

The 6 Vertex Model and Schubert Polynomials

Alain Lascoux
Université de Marne-La-Vallée, 77454, Marne-La-Vallée, France

Received October 24, 2006; Published online February 23, 2007

Abstract
We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.

Key words: alternating sign matrices; Young tableaux; staircases; Schubert polynomials; integrable systems.

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