Affine Stanley symmetric functions

Details Affine Stanley symmetric functions Affine Stanley symmetric functions

2005-01-21

arxiv.org/abs/math/0501335v1

Mathematics

Combinatorics

27 pages

Scientific paper

We define a new family of symmetric functions which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine Schur functions. As applications, we show how affine Stanley symmetric functions generalise the (dual of the) $k$-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. Conjecturally, affine Stanley symmetric functions should be related to the cohomology of the affine flag variety.

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