Let $H$
be a subgroup of a group $G$
. For an irreducible representation $\sigma$
of $H$
, the triple $(G,H, \sigma)$
is called a Gelfand triple if $\sigma$
appears at most once in any irreducible representation of $G$
. Given a triple, it is usually difficult to determine whether a given triple is a Gelfand triple. One has a sufficient condition which is geometric in nature to determine if a given triple is a Gelfand triple, called Gelfand criterion. We will discuss some examples of the Gelfand triple which give us multiplicity one theorem for non-degenerate Whittaker models of ${\mathrm GL}_n$
over finite chain rings, such as $\mathbb{Z}/p^n\mathbb{Z}$
.
This is a joint work with Pooja Singla.