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Unimodality and Lie Superalgebras
Author(s) -
Stanley Richard P.
Publication year - 1985
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1985723263
Subject(s) - mathematics , unimodality , rectangle , lie superalgebra , combinatorics , class (philosophy) , representation theory , lattice (music) , lie algebra , pure mathematics , property (philosophy) , discrete mathematics , algebra over a field , affine lie algebra , current algebra , geometry , computer science , physics , philosophy , epistemology , artificial intelligence , acoustics
It is well‐known how the representation theory of the Lie algebra sl(2, ℂ) can be used to prove that certain sequences of integers are unimodal and that certain posets have the Sperner property. Here an analogous theory is developed for the Lie superalgebra osp(1,2). We obtain new classes of unimodal sequences (described in terms of cycle index polynomials) and a new class of posets (the “super analogue” of the lattice L ( m,n ) of Young diagrams contained in an m × n rectangle) which have the Sperner property.