This article is cited in 5 papers

Multivariate Chebyshev polynomials in terms of singular elements

V. D. Lyakhovsky

Saint Petersburg State University, St. Petersburg, Russia

Abstract: 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.

DOI: 10.4213/tmf8490

 English version: Theoretical and Mathematical Physics, 2013, 175:3, 797–805

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