Building of GL(m, D) and centralizers

被引：22

作者：

Broussous P. ^{[1
]}

Lemaire B. ^{[2
]}

机构：

[1] Département De Mathématiques, Université De Poitiers, BD Marie Et Pierre Curie, 86962 Futuroscope Chasseuneuil Cedex

[2] Mathématique, Université De Paris-Sud, Bat. 425

来源：

Transformation Groups | 2002年 / 7卷 / 1期

关键词：

Topological Group; Field Extension; Division Algebra; Central Division; Central Division Algebra;

D O I：

10.1007/BF01253463

中图分类号：

学科分类号：

摘要：

Let G = GL(m, D) where D is a central division algebra over a commutative nonarchimedean local field F. Let E/F be a field extension contained in M(m, D). We denote by I (resp. IE) the nonextended affine building of G (resp. of the centralizer of E× in G). In this paper we prove that there exists a unique GE-equivariant affine map jE: IE → I. It is injective and its image coincides with the set of E×-fixed points in I. Moreover, we prove that jE is compatible with the Moy-Prasad filtrations.

引用

页码：15 / 50

页数：35

共 19 条

[1]

Broussous P., Minimal strata for GL(m, D), J. reine Angew. Math., 514, pp. 199-236, (1999)

[2]

Bushnell C.J., Kutzko P., The admissible dual of GL<sub>N</sub> via compact open subgroups, Annals of Math. Studies, 129, (1993)

[3]

Bushnell C.J., Kutzko P., (1996)

[4]

Bushnell C.J., Kutzko P., Smooth representations of reductive p-adic groups: Structure theory via types, (1996)

[5]

Bruhat F., Tits J., Groupes réductifs sur un corps local I. Données radicielles valuées, Publ. Math. I.H.E.S., 41, pp. 5-252, (1972)

[6]

Bruhat F., Tits J., Groupes réductifs sur un corps local, II. Sehémas en groupes. Existence d'une donnée radicielle valuée, Publ. Math. I.H.E.S., 60, pp. 5-184, (1984)

[7]

Bruhat F., Tits J., Schémas en groupes et immeubles des groupes classiques sur un corps local, Bull. Soc. Math. France, 112, pp. 259-301, (1984)

[8]

Curtis C.W., Reiner I., Methods of Representation Theory, 1, (1990)

[9]

Frohlich A., Principal orders and embedding of local fields in simple algebras, Proc. London Math. Soc., 54, 3, pp. 247-266, (1987)

[10]

Howe R., Tamely ramified supercuspidal representations of GL<sub>n</sub>, Pacific J. Math., 73, 2, pp. 437-460, (1977)

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