MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

2 Fix typo in the title

1

# restriction of a repreentation of GL(n) to GL(n-1)

Let $R$ be real numbers and consider an irreducible unitary representation (\pi,V) of $GL_n(R)$ in some Hilbert space $V$, now $GL_{n-1}(R)$ embeds in $GL_n(R)$ on the left upper diagonal block.

Now I wanna ask properties of the restrictions of $V$ to $GL_{n-1}$. This representation is not irreducible, so we may ask is it possible to say something about the closed invariant subspaces? Does this restriction have a multiplicity free decomposition?

Note that we can ask the same question for other irreducible Banach or Frechet representation of $GL_n$, or replacing real numbers by complex or p-adic numbers.