Crystal structures for double Stanley symmetric functions
The electronic journal of combinatorics, Tome 27 (2020) no. 3
We relate the combinatorial definitions of the type $A_n$ and type $C_n$ Stanley symmetric functions, via a combinatorially defined "double Stanley symmetric function," which gives the type $A$ case at $(\mathbf{x},\mathbf{0})$ and gives the type $C$ case at $(\mathbf{x},\mathbf{x})$. We induce a type $A$ bicrystal structure on the underlying combinatorial objects of this function which has previously been done in the type $A$ and type $C$ cases. Next we prove a few statements about the algebraic relationship of these three Stanley symmetric functions. We conclude with some conjectures about what happens when we generalize our constructions to type $C$.
@article{10_37236_8872,
author = {Graham Hawkes},
title = {Crystal structures for double {Stanley} symmetric functions},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/8872},
zbl = {1444.05143},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8872/}
}
Graham Hawkes. Crystal structures for double Stanley symmetric functions. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8872
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