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

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 $\displaystyle U_{\mid Y}$.

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