The mixed Poincaré series of generic PGL_n-character stacks is conjectured, proved at Euler specialization, and shown to interpolate structure coefficients of orbital complexes on PGL_n(F_q) and character sheaves on SL_n(F_q).
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$\mathrm{PGL}_n(\mathbb{C})$-character stacks and Langlands duality over finite fields
The mixed Poincaré series of generic PGL_n-character stacks is conjectured, proved at Euler specialization, and shown to interpolate structure coefficients of orbital complexes on PGL_n(F_q) and character sheaves on SL_n(F_q).