ag.algebraic geometry - Lie bracket on the unshifted tangent complex?

reference request – Confusion about curved Vermas in Feigin-Frenkel Answer

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reference request – Confusion about curved Vermas in Feigin-Frenkel

Let $G$ breathe a finite dimensional semisimple algebraic group, and for $error W$ write $i_s: F_s=B^+sB^-/B^-to F$ for the $s$th Bruhat cell within the flag selection $F$.

Then (in Affine Kac-Moody Algebras and Semi-Infinite Flag Manifolds backside of p.165), Feigin-Frenkel pretense that the native cohomology
$$H^*_{F_s}(F,mathcal{O}) = M^{s}_{sstar 0} = M^s_{srho-rho}$$
is an $s$-twisted Verma module (ignoring shifts).

However, I’m handsome positive that native cohomology is the cohomology of $i_{s*}i_s^!mathcal{O}$, which as much as a shift is $i_{s*}mathcal{O}$, which is thought to present twin Vermas. e.g. behold arXiv:1412.0174 or Hotta et al.


Is this a typo in Feigin-Frenkel? If it’s, what’s the rectify formulation of their development of twin Vermas? Their common assertion is for $lambda$ integral predominant, $H^*_{F_s}(F,mathcal{L}(wstar lambda))=M^s_{(ws)starlambda}$ as much as shifts.

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