arXiv subjects

P. Polo

Publications and source records attributed to P. Polo.

2 recordsLinked to original sources

arXiv2000

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

We show that for $p$small highest weight $λ$, 1) there is a $\Z_p$-integral version of the Bernstein-Gelfand-Gelfand complex, still a direct summand subcomplex of the standard complex for $V(λ)$ 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.

math.RT↗

arXiv2000

Résolutions de Demazure affines et formule de Casselman-Shalika géométrique

We prove a conjecture of Frenkel, Gaitsgory, Kazhdan and Vilonen, related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a a split reductive group. Our proof is an extension of the proof given by the first author in the case of GL(n) (see math/9801109); it relies on the study of certain resolutions of Schubert varieties in the affine Grassmannian, built from the so-called minuscule or quasi-minuscule cases.

math.AG↗