The graded center of Z[GA_n(q)] has n-independent structure constants at maximal reflection length, yielding a universal stable center G(q).
Reflection length in the general linear and affine groups
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abstract
We give an intrinsic criterion to tell whether a reflection factorization in the general linear group is reduced, and give a formula for computing reflection length in the general affine group.
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Stability of the centers of group algebras of general affine groups $GA_n(q)$
The graded center of Z[GA_n(q)] has n-independent structure constants at maximal reflection length, yielding a universal stable center G(q).