Algebras of matrix differential operators

JUAN TIRAO

San Pedro, Brasil

Congreso; XVIII Latin American Algebra Colloquium; 2009

If W=W(t) is a matrix weight on the real line and Pn is an orthogonal sequence of matrix valued polynomials we consider the algebra D(W) of all matrix differential operators D such that each Pn is an eigenfunction of D, where the eigenvalue is a matrix. After presenting some general and interesting properties of any D(W), we study in more detail and example, where the weight W is of Hermite type and of size 2x2. This is the first example where D(W) has been computed.