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Atoms and charge in type $C_2$
Patimo, Leonardo1; Torres, Jacinta2
1 University of Pisa L.go B. Pontecorvo 5 56127 Pisa (PI) Italy
2 Jagiellonian University in Kraków Department of Mathematics ul. prof. Stanisława Łojasiewicza 6 30-348 Kraków Poland
Algebraic Combinatorics, Volume 8 (2025) no. 2, pp. 521-574.

We construct atomic decompositions for crystals of type $C_{2}$ and use them to define a charge statistic, thus providing positive combinatorial formulas for the corresponding Kostka–Foulkes polynomials. Our methods include Kashiwara–Nakashima tableaux combinatorics as well as the combinatorics of string polytopes and twisted Bruhat graphs.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.411
Classification: 10X99, 14A12, 11L05
Keywords: crystals, charge

Patimo, Leonardo 1; Torres, Jacinta 2

1 University of Pisa L.go B. Pontecorvo 5 56127 Pisa (PI) Italy
2 Jagiellonian University in Kraków Department of Mathematics ul. prof. Stanisława Łojasiewicza 6 30-348 Kraków Poland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Patimo, Leonardo; Torres, Jacinta. Atoms and charge in type $C_2$. Algebraic Combinatorics, Volume 8 (2025) no. 2, pp. 521-574. doi : 10.5802/alco.411. https://alco.centre-mersenne.org/articles/10.5802/alco.411/

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