Geodesic
Multivariate Chebyshev polynomials in terms of singular elements
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 419-428

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We use the direct correspondence between Weyl anti-invariant functions and multivariate second-type Chebyshev polynomials to substantially simplify most operations with multivariate polynomials. We illustrate the obtained results by studying bivariate polynomials of the second type for root systems $A_1\oplus A_1$, $B_2$, and $G_2$.
Keywords: generalized Chebyshev polynomial, semisimple Lie algebra, representation theory, Weyl group. 
@article{TMF_2013_175_3_a9,
     author = {V. D. Lyakhovsky},
     title = {Multivariate {Chebyshev} polynomials in terms of singular elements},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {419--428},
     publisher = {mathdoc},
     volume = {175},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a9/}
}
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V. D. Lyakhovsky. Multivariate Chebyshev polynomials in terms of singular elements. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 419-428. http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a9/