Symmetry Classes of Polynomials

Esmaeil Babaei, Yousef Zamani*, Mohammad Shahryari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Let G be a subgroup of Sm and suppose χ is an irreducible complex character of G. Let Hd(G, χ) be the symmetry class of polynomials of degree d with respect to G and χ. Let V be an (d + 1)-dimensional inner product space over ℂ and Vχ(G) be the symmetry class of tensors associated with G and χ. A monomorphism Hd(G, χ) → Vχ(G) is given and it is used to obtain necessary and sufficient conditions for nonvanishing Hd(G, χ). The nonexistence of o-basis of Hd(Sm, χπ) for a certain class of irreducible characters of Sm is concluded. The dimensions of symmetry classes of polynomials with respect to the irreducible characters of Sm and Am are computed.

Original languageEnglish
Pages (from-to)1514-1530
Number of pages17
JournalCommunications in Algebra
Volume44
Issue number4
DOIs
Publication statusPublished - Apr 2 2016
Externally publishedYes

Keywords

  • Alternating group
  • Irreducible characters
  • Orthogonal basis
  • Symmetric group
  • Symmetry class of polynomials
  • Symmetry class of tensors

ASJC Scopus subject areas

  • Algebra and Number Theory

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