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Tensor species and symmetric functions.

Authors
  • Méndez, M
Type
Published Article
Journal
Proceedings of the National Academy of Sciences
Publisher
Proceedings of the National Academy of Sciences
Publication Date
Nov 01, 1991
Volume
88
Issue
21
Pages
9892–9894
Identifiers
PMID: 11607233
Source
Medline
License
Unknown

Abstract

An equivariant representation of the symmetric group Sn (equivariant representation from here on) is defined as a particular type of tensor species. For any tensor species R the characteristic generating function of R is defined in a way that generalizes the Frobenius characters of representations of the symmetric groups. If R is an equivariant representation, then the characteristic is a homogeneous symmetric function. The combinatorial operations on equivariant representations correspond to formal operations on the respective characteristic functions. In particular, substitution of equivariant representations corresponds to plethysm of symmetric functions. Equivariant representations are constructed that have as characteristic the elementary, complete, and Schur functions. Bijective proofs are given for the formulas that connect them with the monomial symmetric functions.

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