This article is cited in 2 papers

Numerical constructions involving Chebyshev polynomials

V. D. Lyakhovsky

St. Petersburg State University, St. Petersburg, Russia

Abstract: We propose a new algorithm for the character expansion of tensor products of finite-dimensional irreducible representations of simple Lie algebras. The algorithm produces valid results for the algebras $B_3$, $C_3$, and $D_3$. We use the direct correspondence between Weyl anti-invariant functions and multivariate second-kind Chebyshev polynomials. We construct the triangular trigonometric polynomials for the algebra $D_3$.

Keywords: algebra representation, fundamental module, three-dimensional Lie algebra, Chebyshev polynomial.

Received: 09.12.2015
Revised: 25.04.2016

DOI: 10.4213/tmf9116

 English version: Theoretical and Mathematical Physics, 2017, 190:2, 303–314

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