Orbit functions of SU(n) and Chebyshev polynomials

Details Orbit functions of SU(n) and Chebyshev polynomials Orbit functions of SU(n) and Chebyshev polynomials

2009-05-18

arxiv.org/abs/0905.2925v2

Mathematics

Classical Analysis and ODEs

15 pages, we have rewritten and reorganized all the manuscript

Scientific paper

Orbit functions of a simple Lie group/Lie algebra L consist of exponential functions summed up over the Weyl group of L. They are labeled by the highest weights of irreducible finite dimensional representations of L. They are of three types: C-, S- and E-functions. Orbit functions of the Lie algebras An, or equivalently, of the Lie group SU(n+1), are considered. First, orbit functions in two different bases - one orthonormal, the other given by the simple roots of SU(n) - are written using the isomorphism of the permutation group of n elements and the Weyl group of SU(n). Secondly, it is demonstrated that there is a one-to-one correspondence between classical Chebyshev polynomials of the first and second kind, and C- and $S$-functions of the simple Lie group SU(2). It is then shown that the well-known orbit functions of SU(n) are straightforward generalizations of Chebyshev polynomials to n-1 variables. Properties of the orbit functions provide a wealth of properties of the polynomials. Finally, multivariate exponential functions are considered, and their connection with orbit functions of SU(n) is established.

Affiliated with

Also associated with

No associations

Rating

Orbit functions of SU(n) and Chebyshev polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orbit functions of SU(n) and Chebyshev polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orbit functions of SU(n) and Chebyshev polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-610101