Abstract
Given a finite ranked poset P, for each rank of P a space of complex valued functions on P called harmonics is defined. If the automorphism group G of P is sufficiently rich, these harmonic spaces yield irreducible representations of G. A decomposition theorem, which is analogous to the decomposition theorem for spherical harmonics, is stated. It is also shown that P can always be decomposed into posets whose principal harmonics are orthogonal polynomials. Classical examples are given.
Original language | English (US) |
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Pages (from-to) | 136-149 |
Number of pages | 14 |
Journal | Journal of Combinatorial Theory, Series A |
Volume | 40 |
Issue number | 1 |
DOIs | |
State | Published - Sep 1985 |
Bibliographical note
Funding Information:supported by NSF Grant MCS 834872.