# Thread: What does \upharpoonright mean?

1. ## What does \upharpoonright mean?

Hello friends,

While reading the book Representations of Finite and Compact Groups by Barry Simon I came upon the notation $\upharpoonright$ which he fails to define. From context I would guess it means "restriction" but I can't be sure. For example here's some context

Let $U:G\to V$ be a representation of $G$ on $V$ and suppose that $W\leqslant V$ is invariant under $U$. Then, $U\upharpoonright W$ and $U\upharpoonright W^{\perp}$ define representations $U_1$ and $U_2$ and $U$ is equivalent to $U_1\oplus U_2$

2. Yes - that symbol is generally used to restrict a function to a smaller domain.

3. Originally Posted by DrSteve
Yes - that symbol is generally used to restrict a function to a smaller domain.
Strange, I have ALWAYS (and I've looked through a few books in my time) seen $U_{\mid Y}$.

4. I actually use both notations pretty regularly, but I don't remember where and when I learned to use each of them.