Total characters and Chebyshev polynomials
Copyright policy )Total characters and Chebyshev polynomials
The total character τ of a finite group G is defined as the sum of all the irreducible characters of G. K. W. Johnson asks when it is possible to express τ as a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson′s question for all finite dihedral groups. In particular, we show that, when such a polynomial exists, it is unique and it is the sum of certain Chebyshev polynomials of the first kind in any faithful irreducible character of the dihedral group G.
- State University System of Florida United States
- New College of Florida United States
Ordinary representations and characters, total characters, QA1-939, irreducible characters, Connections of hypergeometric functions with groups and algebras, and related topics, Chebyshev polynomials, finite dihedral groups, Mathematics, Gelfand models
Ordinary representations and characters, total characters, QA1-939, irreducible characters, Connections of hypergeometric functions with groups and algebras, and related topics, Chebyshev polynomials, finite dihedral groups, Mathematics, Gelfand models
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