Séminaire Lotharingien de Combinatoire, 93B.4 (2025), 12 pp.
Álvaro Gutiérrez
Towards Plethystic sl2 Crystals
Abstract.
To find crystals of sl2 representations of the form
ΛnSymrC2 it suffices to solve the
combinatorial problem of decomposing Young's lattice into
rank-symmetric chains. We review the literature on this latter
problem, and present a strategy to solve it. For n ≤ 4, the
strategy recovers recently discovered solutions. We obtain (i)
counting formulas for plethystic coefficients, (ii) new recursive
formulas for plethysms of Schur functions, and (iii) formulas for the
number of constituents of ΛnSymrC2.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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