See for example <https://www.sciencedirect.com/science/article/pii/0021869387901542> for the definition of the Lusztig a-function.



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> Question 1: Is there a table for the values of Lusztig's a-function for a given Dynkin type?
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Can one at least find those values when the corresponding simple Lie-algebra has rank <=4? I try to find a reference for the case $G\_2$ especially.



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> Question 2: Is there a computer program to calculate those values for small Dynkin types?
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Computation of the Lusztig a-function
In Addition to Geck-Pfeiffer: Small values of the **a**-function are also contained in Geck, Jacon - Representations of Hecke algebras at roots of unity. In particular, for $G\_2$ it's in Table 1.3.; for $F\_4$ it's table 1.2.; other values are available through combinatorially formulas (for example type $A$ is completely covered in section 2.8) and Remark 1.3.11 contains a fairly straight-forward algorithm to compute the **a**-function in general.


