Geodesic
Crystal analysis of type \(C\) Stanley symmetric functions
Graham Hawkes1 ; Kirill Paramonov1 ; Anne Schilling1
1University of California at Davis
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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Combining results of T.K. Lam and J. Stembridge, the type $C$ Stanley symmetric function $F_w^C(\mathbf{x})$, indexed by an element $w$ in the type $C$ Coxeter group, has a nonnegative integer expansion in terms of Schur functions. We provide a crystal theoretic explanation of this fact and give an explicit combinatorial description of the coefficients in the Schur expansion in terms of highest weight crystal elements.
DOI : 10.37236/6952
Classification : 05E05, 20G42
Mots-clés : Stanley symmetric functions, crystal bases, Kraśkiewicz insertion, mixed Haiman insertion, unimodal tableaux, primed tableaux

Graham Hawkes  1   ; Kirill Paramonov  1   ; Anne Schilling  1

1 University of California at Davis 
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     author = {Graham Hawkes and Kirill Paramonov and Anne Schilling},
     title = {Crystal analysis of type {\(C\)} {Stanley} symmetric functions},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {3},
     doi = {10.37236/6952},
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Graham Hawkes; Kirill Paramonov; Anne Schilling. Crystal analysis of type \(C\) Stanley symmetric functions. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6952

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