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- W1944149689 abstract "For a reductive Lie algebra ({mathfrak {h}}) and a simple finite-dimensional ({mathfrak {h}})-module V, the set of weights of (V,,mathcal {P}(V)), is equipped with a natural partial order. We consider antichains in the weight poset (mathcal {P}(V)) and a certain operator (mathfrak {X}) acting on antichains. Eventually, we impose stronger constraints on (({mathfrak {h}},V)) and stick to the case in which ({mathfrak {h}}={mathfrak {g}}(0)) and (V={mathfrak {g}}(1)) for a ({mathbb {Z}})-grading ({mathfrak {g}}=bigoplus _{iin {mathbb {Z}}}{mathfrak {g}}(i)) of a simple Lie algebra ({mathfrak {g}}). Then V is a weight multiplicity free ({mathfrak {h}})-module and (mathcal {P}(V)) can be regarded as a subposet of (Delta ^+), where (Delta ) is the root system of ({mathfrak {g}}). Our goal is to demonstrate that the weight posets associated with ({mathbb {Z}})-gradings exhibit many good properties that are similar to those of (Delta ^+) that are observed earlier in Panyushev (Eur J Combin 30(2):586–594, 2009)." @default.
- W1944149689 created "2016-06-24" @default.
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- W1944149689 date "2015-09-19" @default.
- W1944149689 modified "2023-09-26" @default.
- W1944149689 title "Antichains in weight posets associated with gradings of simple Lie algebras" @default.
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- W1944149689 doi "https://doi.org/10.1007/s00209-015-1527-3" @default.
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