A subscript is indicated by the underscore ``_''. For example,
$\alpha_j$ | gives |  |
$\alpha^j$ | gives |  |
$\alpha_j^i$ | gives |  |
$\alpha_{j^i}$ | gives | |
{}.
They are used a lot in math mode to group things together.
Many math commands in 
are defined to operate on
the next item which appears in the file: either a single
letter, a command word, or a group delimitted by braces.
For instance, the subscripting
operator ``_'' can be used to subscript a single
letter ($a_b$) or a single command
($a_\beta$). But if you want a subscript
containing something more complicated, say 
,
then you must use braces: $a_{b+\beta}$.
Another example of when the curly braces must be used is if you want the subscripts lower and smaller. Then, you would type
$\alpha_{_j}$.
.
$\alpha__j$ will generate an
error message.