Legendre polynomials and the elliptic genus (Q1183283)

\textit{J. Dieudonné} [``Special functions and linear representations of Lie groups,'' (1980; Zbl 0425.22018)] shows that Legendre polynomials can be interpreted as matrix coefficients for finite-dimensional representations of the algebraic group \(SL(2)\). By taking modulo \(p\) of thus representations, the author gives the representation-theoretic interpretations of Schur congruences and some of Honda's congruences, given by \textit{T. Honda} [Osaka J. Math. 3, 131-133 (1976; Zbl 0345.12101)], for the Legendre polynomials. Moreover, he suggests that there might exist some deeper connection between \(GL(2)\) and the elliptic genus.