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Total characters and Chebyshev polynomials

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  • Eirini Poimenidou
  • Homer Wolfe

Abstract

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 .

Suggested Citation

  • Eirini Poimenidou & Homer Wolfe, 2003. "Total characters and Chebyshev polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:384016
    DOI: 10.1155/S0161171203201046
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