what does the alpha symbol represent in the standard equation used for inference by enumeration can anyone tell me what the alpha means in the following equation (used for inference by enumeration)?


Based on the equation it could have meant $1/P(e)$ as the RHS sum is the joint distribution of $e$ and Cause; if every distribution/probability here was well-defined. But, apparently, we don't know it.
As rightly pointed out the in the comments, the notation used here is vague. $P(e)$, more explicit alternative might be $P_e(e')$, where $e$ represents the random variable/vector and $e'$ is one particular realization, and $P_e$ represents the PDF or PMF function of the random object $e$. Similar concern is valid for other expressions in the formula. This makes it harder to accurately answer the question.
The logic $\alpha$ being $1/P(e)$ stems from the following relation (assume $X,Y,Z$ are discrete RVs for simplicity):
$$p_{X|Y}(x|y)=\frac{p_{X,Y}(x,y)}{p_Y(y)}=\underbrace{\frac{1}{p_Y(y)}}_\alpha\sum_{z}p_{X,Y,Z}(x,y,z)$$
So, considering we're interested in some RV or event, $X$, the denominator, i.e. $\alpha$ becomes merely normalizing constant, i.e. a scaler.
