Unimodality and Lie superalgebras. (English) Zbl 0614.17004
Representation theory of Lie algebras has previously been used to prove that certain sequences of numbers related to their representations are unimodal, and that certain partially ordered sets have the Sperner property. In this paper analogues of such results are obtained relating to Lie superalgebras, leading to unimodality results for new classes of sequences, and the Spernerity of a (two) new class(es) of partially ordered sets: Young tableau defined on a given rectangle that have at most one row of each even (odd) size.
Reviewer: D.Kleitman
MSC:
| 17A70 | Superalgebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 06A06 | Partial orders, general |
| 05A99 | Enumerative combinatorics |
Keywords:
orthosymplectic superalgebra; representations; Sperner property; Lie superalgebras; unimodality; partially ordered sets; Young tableauReferences:
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