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math.NT2026
A resolution of the Steinberg module of a parabolic subgroup of GL_n
Avner Ash, Paul E. Gunnells
Let F be a field, G = GL_n(F), and let St be the Steinberg module of G. For a parabolic subgroup P of G, let St_P be its Steinberg module. There is a natural map rho_P: St -> St_P…
math.NT2024
Cohomology with Sym^g coefficients for congruence subgroups of SL_4(Z) and Galois representations
Avner Ash, Paul E. Gunnells, Mark McConnell
We extend the computations in our prior work to find the cohomology in degree five of a congruence subgroup Gamma of SL_4(Z) with coefficients in Sym^g(K^4), twisted by a nebentype…