Symmetry Classes of Polynomials

Esmaeil Babaei; Yousef Zamani; Mohammad Shahryari

doi:10.1080/00927872.2015.1027357

Symmetry Classes of Polynomials

Esmaeil Babaei, Yousef Zamani^*, Mohammad Shahryari

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let G be a subgroup of S_m and suppose χ is an irreducible complex character of G. Let H_d(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 V_χ(G) be the symmetry class of tensors associated with G and χ. A monomorphism H_d(G, χ) → V_χ(G) is given and it is used to obtain necessary and sufficient conditions for nonvanishing H_d(G, χ). The nonexistence of o-basis of H_d(S_m, χ^π) for a certain class of irreducible characters of S_m is concluded. The dimensions of symmetry classes of polynomials with respect to the irreducible characters of S_m and A_m are computed.

Original language	English
Pages (from-to)	1514-1530
Number of pages	17
Journal	Communications in Algebra
Volume	44
Issue number	4
DOIs	https://doi.org/10.1080/00927872.2015.1027357
Publication status	Published - Apr 2 2016

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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10.1080/00927872.2015.1027357

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title = "Symmetry Classes of Polynomials",

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.",

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AU - Babaei, Esmaeil

AU - Zamani, Yousef

AU - Shahryari, Mohammad

PY - 2016/4/2

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N2 - 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.

AB - 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.

KW - Alternating group

KW - Irreducible characters

KW - Orthogonal basis

KW - Symmetric group

KW - Symmetry class of polynomials

KW - Symmetry class of tensors

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Symmetry Classes of Polynomials

Abstract

Keywords

ASJC Scopus subject areas

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