Papers › Affine transitions for involution Stanley symmetric functions
Affine transitions for involution Stanley symmetric functions
Eric Marberg, Yifeng Zhang
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We study a family of symmetric functions F̂_z indexed by involutions z in the affine symmetric group. These power series are analogues of Lam's affine Stanley symmetric functions and generalizations of the involution Stanley symmetric functions introduced by Hamaker, Pawlowski, and the first author. Our main result is to prove a transition formula for F̂_z which can be used to define an affine involution analogue of the Lascoux-Sch\"utzenberger tree. Our proof of this formula relies on Lam and Shimozono's transition formula for affine Stanley symmetric functions and some new technical properties of the strong Bruhat order on affine permutations.
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