Truncations of level 1 of elements in the loop group of a reductive group
By E. Viehmann. 2009
62 citations recorded by the source corpus.
The aim of this article is to dene and study a new invariant of elements of loop groups that is invariant under -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 -conjugacy classes obtained from elements of a given truncation of level 1 and in particular for the generic -conjugacy class in any given truncation stratum. In the last section we relate our invariant to the Ekedahl-Oort stratication of the Siegel moduli space and to generalizations to other PEL Shimura varieties.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7ae2ae229c512729b882f044025c16770ee4e004
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In Geometry and Topology
- Xuhua He
- E. Viehmann
- Michael Rapoport
- Thomas J. Haines
- Ulrich Goertz
- R. Kottwitz
- Daniel C. Reuman
- T. Wedhorn
In Mathematical Physics
- Xuhua He
- E. Viehmann
- Michael Rapoport
- Thomas J. Haines
- Ulrich Goertz
- R. Kottwitz
- Daniel C. Reuman
- T. Wedhorn
Citations in the corpus
- Affine Deligne–Lusztig varieties in affine flag varieties (2008, methodology): “nt in the function field and the p-adic case (Corollary 11.3.5). While this was certainly expected to hold, to the best of our knowledge no proof was known before. This equivalence is used by Viehmann [V3] to investigate closure relations for Ekedahl-Oort strata in certain Shimura varieties; our resu”
- Ekedahl–Oort and Newton strata for Shimura varieties of PEL type (2010, methodology): “tial order on JWwhich was introduced by He[He] in his study ofthe spherical completions of reductive groups (see Definition 4.8). This description can also be derived from results of the first author ([Vi1]). In particular the closures and the codimension of points are known. These results are recalle”
- Stratifications in the reduction of Shimura varieties (2015, methodology): “(2) IfG is unramified andK is hyperspecial, the definition of the EKOR stratification coincides with the Ekedahl-Oort stratification in the sense of Viehmann [46].”