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.

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Last updated: 08 Dec 2021