What does \upharpoonright mean?

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January 12th 2011, 07:18 PM
Drexel28

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

Quote:

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 $U_1\oplus U_2$
January 13th 2011, 02:51 AM
DrSteve

Yes - that symbol is generally used to restrict a function to a smaller domain.
January 13th 2011, 09:34 AM
Drexel28

Quote:

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 $U_{\mid Y}$ .
January 13th 2011, 09:40 AM
DrSteve

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