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June 3 - Masseh Mathematics & Statistics Colloquium: The tail condition for Leonard pairs
Author: Fariborz Maseeh Department of Mathematics and Statistics
Posted: June 1, 2016

Fariborz Maseeh Department of Mathemtics and Statistics and
The Maseeh Mathematics and Statistics Colloquium Series*
present

Edward Hanson, Ph.D.
Department of Mathematics
State University of New York - New Paltz

The tail condition for Leonard pairs

Abstract:
Let V denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations A:V→V and A*:V→V that satisfy the following conditions:

  • There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A* is diagonal.
  • There exists a basis for V with respect to which the matrix representing A* is irreducible tridiagonal and the matrix representing A is diagonal.

We call such a pair a Leonard pair on V. Roughly speaking, a Leonard pair can be thought of as an algebraic generalization of a Q-polynomial distance-regular graph. In this talk, we will discuss characterizations of Leonard pairs that utilize the notion of a tail. This notion is borrowed from algebraic graph theory.

Friday, June 3, 2016 at 2 p.m.
Neuberger Hall 454
(Refreshments served at 2:45 p.m. in NH 344 downstairs)

* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.