Geodesic
The virtual cactus group and Littelmann paths
Jacinta Torres1
1Jagiellonian University, Department of Mathematics
The electronic journal of combinatorics, Tome 31 (2024) no. 1

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Zbl DOI arXiv
We define a virtual cactus group and show that the cactus group action on Littelmann paths is compatible with the virtualization map defined by Pan-Scrimshaw. To show this we use the combinatorics of Dynkin diagram foldings. Our definition generalizes the group with the same name recently defined for the symplectic Lie algebra in recent joint work with Azenhas and Tarighat-Feller.
DOI : 10.37236/12034
Classification : 05E10, 05E05, 17B37, 17B67
Mots-clés : Kac-Moody algebra, virtual crystals, Kleber's algorithm, quantized enveloping algebra

Jacinta Torres  1

1 Jagiellonian University, Department of Mathematics 
Jacinta Torres. The virtual cactus group and Littelmann paths. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12034
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     title = {The virtual cactus group and {Littelmann} paths},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {1},
     doi = {10.37236/12034},
     zbl = {1533.05292},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12034/}
}
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