AFFINE STANLEY SYMMETRIC FUNCTIONS By THOMAS LAM
نویسنده
چکیده
We define a new family F̃w(X) of generating functions for w ∈ S̃n 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 generalize 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.
منابع مشابه
A Little Bijection for Affine Stanley Symmetric Functions
Little [Adv. Math. 174 (2003), 236–253] developed a combinatorial algorithm to study the Schur-positivity of Stanley symmetric functions and the Lascoux–Schützenberger tree. We generalize this algorithm to affine Stanley symmetric functions, which were introduced recently in [T. Lam: “Affine Stanley symmetric functions,” Amer. J. Math., to appear].
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