Typing (and executing) expressions with multiple superscripts

Question

I am trying to type (and evaluate) expressions of the following form:

$$ G^{a,b} $$

into a mathematica. I've tried the obvious

G^(a, b)

or

Superscript[G,a,b]

But both of these give the same error

Syntax::tsntxi: "a,b" is incomplete; more input is needed.

I know one solution is to use Symbolize from the Notation package

<< Notation`
Symbolize[ParsedBoxWrapper[SuperscriptBox["G", RowBox[{"_", ",", "_"}]]]]

however this solution will not suffice as I want to perform operations such as the following:

In[3]:= Sum[G^(a, b), {a, 1, 2}, {b, 1, 2}]
Out[3]= 4 G^(a, b)

Is there any sensible way to get around this? Why is Superscript so much more picky than Subscript? Thanks in advance.

Answer 1

Perhaps this will work for you:

MakeBoxes[Superscript[b_, x_, y__], form_] ^:=
  ToBoxes[Superscript[b, Row[{x, y}]], form]

Example:

Sum[Superscript[G, a, b], {a, 1, 2}, {b, 1, 2}]

$G^{11}+G^{12}+G^{21}+G^{22}$