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Appendix B of Randal-Williams' "Cohomology of automorphism groups of free groups with twisted coefficients" gives a stable description of the graded $\mathbb{Q}[\Sigma_k]$$\mathbb{Q}[\Sigma_q]$-module $H^*(\Gamma_g;H^{\otimes q})$.
Appendix B of Randal-Williams' "Cohomology of automorphism groups of free groups with twisted coefficients" gives a stable description of the graded $\mathbb{Q}[\Sigma_k]$-module $H^*(\Gamma_g;H^{\otimes q})$.
Appendix B of Randal-Williams' "Cohomology of automorphism groups of free groups with twisted coefficients" gives a stable description of the graded $\mathbb{Q}[\Sigma_q]$-module $H^*(\Gamma_g;H^{\otimes q})$.
