Truncations of level 1 of elements in the loop group of a reductive group

• Autores: Eva Viehmann
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 179, Nº 3, 2014, págs. 1009-1040
• Idioma: inglés
• DOI: 10.4007/annals.2014.179.3.3
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• Resumen

  • The aim of this article is to define and study a new invariant of elements of loop groups that is invariant under s -conjugation by a hyperspecial maximal open subgroup and that we call the truncation of level 1. We classify truncations of level 1 and describe their specialization behavior. Furthermore, we prove group-theoretic conditions for the set of s -conjugacy classes obtained from elements of a given truncation of level 1 and in particular for the generic s -conjugacy class in any given truncation stratum. In the last section we relate our invariant to the Ekedahl-Oort stratification of the Siegel moduli space and to generalizations to other PEL Shimura varieties