Speaker
Gabriel Pretel
(University of Wisconsin-Madison, USA)
Description
Roughly speaking, tridiagonal pairs of Krawtchouk type correspond to the finite-dimensional irreducible modules of a certain Lie algebra known as the Onsager algebra. E. Date and S. S. Roan showed that the Onsager algebra is embedded in another Lie algebra known as the sl2 loop algebra. They classified the finite-dimensional irreducible modules for the Onsager algebra, and in particular they showed that every such module is obtained from an sl2 loop algebra module by restriction. It is then natural to consider the various ways of extending a given Onsager algebra module to an sl2 loop algebra module. We consider these extensions and how they are related to one another. To aid in this description we introduce the notion of a compatible element for a tridiagonal pair. We discuss a case in which these extensions have a simple combinatorial interpretation in terms of hypercubes.
Primary author
Gabriel Pretel
(University of Wisconsin-Madison, USA)
