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SL(2,C), SU(2) AND CHEBYSHEV POLYNOMIALS

Authors
  • Bacry, Henri
Publication Date
Dec 01, 1986
Identifiers
DOI: 10.1063/1.527759
OAI: oai:inspirehep.net:239402
Source
INSPIRE-HEP
License
Unknown
External links

Abstract

When expressed in terms of the trace, the characters of SU(2) are known to be related with the Chebyshev polynomials of second kind. It is shown that those of the first kind also play a fundamental role. If A∈SU(2) and t=Tr A, then f n (t)=Tr(A n ), f n (2 cos θ)=sin nθ/sin θ, l n (t) =Tr(A n ), l n (2 cos θ)=2 cos nθ, where A n denotes the representative of A in the irrep of dimension n. Other polynomials related with them are of interest. They are (i) the ‘‘primordial’’ polynomialsP n (every f n or l n can be expressed in a unique way in terms of P d , where d is a divisor of n), (ii) the ‘‘factorial’’ polynomialsf n !=f 1  f 2⋅⋅⋅f n which occur in a natural way in the representations, (iii) the g n polynomials appearing in the generating functions of powers of f n .

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