Orthogonal Polynomials of Compact Simple Lie Groups
Copyright policy )Orthogonal Polynomials of Compact Simple Lie Groups
Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type A1. The obtained not Laurent‐type polynomials are equivalent to the partial cases of the Macdonald symmetric polynomials. Recurrence relations are shown for the Lie groups of types A1, A2, A3, C2, C3, G2, and B3 together with lowest polynomials.
- University of Montreal Canada
- Institute of Mathematics Poland
- Polish Academy of Learning Poland
- Polish Academy of Sciences Poland
- University of Białystok Poland
Symmetric functions and generalizations, simple Lie groups, FOS: Physical sciences, orthogonal multivariate polynomials, Connections of hypergeometric functions with groups and algebras, and related topics, Mathematical Physics (math-ph), Orthogonal polynomials and functions associated with root systems, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Semisimple Lie groups and their representations, Mathematics - Classical Analysis and ODEs, Weyl group, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Chebyshev polynomials, Representation Theory (math.RT), orthogonal polynomials, Mathematics, Mathematical Physics, Mathematics - Representation Theory
Symmetric functions and generalizations, simple Lie groups, FOS: Physical sciences, orthogonal multivariate polynomials, Connections of hypergeometric functions with groups and algebras, and related topics, Mathematical Physics (math-ph), Orthogonal polynomials and functions associated with root systems, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Semisimple Lie groups and their representations, Mathematics - Classical Analysis and ODEs, Weyl group, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Chebyshev polynomials, Representation Theory (math.RT), orthogonal polynomials, Mathematics, Mathematical Physics, Mathematics - Representation Theory
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