Orthogonal Polynomials of Compact Simple Lie Groups
نویسندگان
چکیده
منابع مشابه
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 theMacdonald symmet...
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Three types of numerical data are provided for simple Lie groups of any type and rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of C− or S−functions on the fundamental domain F of the underlying Lie group G. Firstly, we consider the number |FM | of points in F from the lattice P∨ M , which is the refinement of the dual weight lat...
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depending on indeterminates x1, . . . , xn. Dyson conjectured the explicit form of this constant term. His conjecture was soon related with the root system of sl(n), generalized to other root systems of simple Lie algebras and proved. The expressions obtained for the Dyson constant are called Macdonald’s identities, see [M]. Let us briefly recall the main results. Let g be a simple (finite dime...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2011
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2011/969424