Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 078, 9 pages      arXiv:1407.6458      https://doi.org/10.3842/SIGMA.2014.078

Some Noncommutative Matrix Algebras Arising in the Bispectral Problem

F. Alberto Grünbaum
Department of Mathematics, University of California, Berkeley, CA 94720 USA

Received May 01, 2014, in final form July 17, 2014; Published online July 24, 2014

Abstract
I revisit the so called ''bispectral problem'' introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues, to be matrix valued too. In the last example we go beyond this and allow both eigenvalues to be matrix valued.

Key words: noncommutative algebras; bispectral problem.

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