Orthogonal polynomials of compact simple Lie groups

Autor:	Nesterenko, Maryna, Patera, Jiri, Tereszkiewicz, Agnieszka
Rok vydání:	2010
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Representation Theory
Zdroj:	International Journal of Mathematics and Mathematical Sciences Volume 2011 (2011), Article ID 969424, 23 pages
Druh dokumentu:	Working Paper
DOI:	10.1155/2011/969424
Popis:	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 $A_1$. The obtained not Laurent-type polynomials are proved to be equivalent to the partial cases of the Macdonald symmetric polynomials. Basic relation between the polynomials and their properties follow from the corresponding properties of the orbit functions, namely the orthogonality and discretization. Recurrence relations are shown for the Lie groups of types $A_1$, $A_2$, $A_3$, $C_2$, $C_3$, $G_2$, and $B_3$ together with lowest polynomials. Comment: 34 pages, some minor changes were done, to appear in IJMMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1001.3683 Zobrazit plný text záznamu Plný text ve formátu PDF