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Molecules of an affine FPF -graph and a labelled row-Beissinger reconstruction
Yifeng Zhang
Kazhdan--Lusztig -graphs encode the cell structure of Hecke algebras, while their bidirected connected components are called molecules. In finite type~, the Robinson--Schenst…
Dual Weight and Monodromy of Dual Affine RS Correspondence
Yifeng Zhang
The dual affine Robinson--Schensted correspondence and the affine matrix-ball construction give two related parametrizations of extended affine permutations. From the stable-window…
Recursive structures of molecules and cells in Gelfand -graphs
Zhiqiang Dai, Yifeng Zhang
-graphs, representing the multiplication action of the standard basis on the canonical basis in the Iwahori-Hecke algebra are introduced by Kazhdan and Lusztig. Marberg defined…
Insertion algorithms for Gelfand -graphs
Eric Marberg, Yifeng Zhang
The two tableaux assigned by the Robinson--Schensted correspondence are equal if and only if the input permutation is an involution, so the RS algorithm restricts to a bijection be…
Quasiparabolic sets and Stanley symmetric functions for affine fixed-point-free involutions
Yifeng Zhang
We introduce and study affine analogues of the fixed-point-free (FPF) involution Stanley symmetric functions of Hamaker, Marberg, and Pawlowski. Our methods use the theory of quasi…
Affine transitions for involution Stanley symmetric functions
Eric Marberg, Yifeng Zhang
We study a family of symmetric functions indexed by involutions in the affine symmetric group. These power series are analogues of Lam's affine Stanley symmetric fun…