Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over $\Z_p$ for representations with p-small weights

P. Polo (1) , Jacques Tilouine (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We show that for $p$small highest weight $\lambda$, 1) there is a $\Z_p$-integral version of the Bernstein-Gelfand-Gelfand complex, still a direct summand subcomplex of the standard complex for $V(\lambda)$ 2) Similarly, a $\Z_p$-integral (as well as a mod. p) version of Kostant formula holds true. This paper is a companion paper to the one by Mokrane-Tilouine (AG, subm. 12/12/00), where these results are requested.

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

P. Polo, Jacques Tilouine. Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over $\Z_p$ for representations with p-small weights. Asterisque, 2002, 280, pp.97-135. ⟨hal-00133208⟩