國立清華大學 數學系

Abstract: Let K be an algebraically closed field of characteristic zero and V denote a finite dimensional vector space over K. A Leonard triple on V is an ordered triple of linear transformations on V such that for each of these transformations there exists a basis of V with respect to which the matrix representing that transformation is diagonal and the matrices representing the other two transformations are irreducible tridiagonal. Leonard triples are extensions of Leonard pairs, which are combinatorial and linear algebraic objects that have been studied in connection with orthogonal polynomials, association schemes, and representations of certain algebras. In this talk, we will discuss a certain family of Leonard pairs constructed from the standard basis of the Lie algebra sl2 and determine all Leonard triples arising from this pair. Tea Time: 3:00-3:30pm R707 (七樓休息室)