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The classical Eulerian polynomials $A_n(t)$ are known to be gamma positive.Define the positive Eulerian polynomial $A_n^+(t)$ as the polynomial obtainedwhen we sum descents over the alternating group. We show that $A_n^+(t)$ isgamma positive iff $n \equiv 0,1$ (mod 4). When $n \equiv 2$ (mod 4) we showthat $A_n^+(t)$ can be written as a sum of two gamma positive polynomials whileif $n \equiv 3$ (mod 4), we show that $A_n^+(t)$ can be written as a sum ofthree gamma positive polynomials.  Similar results are shown when we consider the positive type-D and type-DEulerian polynomials.

Gamma positivity of the Descent based Eulerian polynomial in positive elements of Classical Weyl Groups