A-like elements for a tridiagonal pair

Gabriel Pretel (University of Wisconsin - Madison, USA)

Given a tridiagonal pair $(A,A^*)$ on a vector space $V$, we say that an element of ${\rm End}(V)$ is $A$-like if it commutes  with $A$ and acts tridiagonally on the eigenspaces of $A^*$.  We give a classification of the $A$-like elements, in the case where $(A,A^*)$ is of Krawtchouk type with shape $(1,2,1)$.