On multiplicity in restriction of tempered representations of p-adic groups

Mathematische Zeitschrift - We establish an equality between two multiplicities: one in the restriction of tempered representations of a p-adic group to its closed subgroup with the same derived...     

On invariants of discrete series representations of classical p-adic groups

To an irreducible square integrable representation ?? of a classical p-adic group, M?glin has attached invariants Jord(??), ?? _cusp and ${\epsilon_\pi}$ . These triples classify square integrable representations modulo cuspidal data (assuming a natural hypothesis). The definition of these invariants in M?glin (J Eur Math Soc 4(2):143?C200, 2002) is rather simple??in terms of induced representations, except at one case when a coherent normalization of standard intertwining operators is required. In this paper we show how one can define this case also in terms of induced representations.     

Barsotti–Tate groups and p-adic representations of the fundamental group scheme

On a scheme S over a base scheme B we study the category of locally constant BT groups, i.e. groups over S that are twists, in the flat topology, of BT groups defined over B. These groups generalize p-adic local systems and can be interpreted as integral p-adic representations of the fundamental group scheme of S/B (classifying finite flat torsors on the base scheme) when such a group exists. We generalize to these coefficients the Katz correspondence for p-adic local systems and show that they are closely related to the maximal nilpotent quotient of the fundamental group scheme.     

Types and Hecke algebras for principal series representations of split reductive p-adic groups

We construct types in the sense of Bushnell and Kutzko for principal series representations of split connected reductive p-adic groups (with mild restrictions on the residual characteristic) and describe the resulting Hecke algebras. We discuss their interpretation as Iwahori Hecke algebras of related reductive groups (in general disconnected). In addition, we describe how (parabolic) induction and (Jacquet) restriction functors and questions about square-integrability can be transferred to this context.     

Integral p-adic representations and representations over a ring of residue classes

Ukrainian Mathematical Journal -     

Structure of p-adic Schottky groups

For an arbitrary p-adic Schottky group , we construct a set of generators g1, ..., gn with the following property: There exists a set of 2n circles I₁ I₁, ..., I_n, I_n in the protective line with disjoint interiors, such that gi maps the exterior of I_i onto the interior of I_i, i=1, ..., n.Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 625–630, November, 1976.In conclusion, I thank Yu. I. Manin for supervising this work and for valuable sug-gestions.     

Definable groups and compact p-adic Lie groups

We formulate p-adic analogues of the o-minimal group conjecturesfrom the works of Hrushovski, Peterzil and Pillay [J. Amer.Math. Soc., to appear] and Pillay [J. Math. Log. 4 (2004) 147–162];that is, we formulate versions that are appropriate for groupsG definable in (saturated) P-minimal fields. We then restrictour attention to saturated models K of Th(_p) and Th(_{p, an}),record some elementary observations when G is defined over thestandard model _p, and then make a detailed analysis of the casewhere G = E(K) for E an elliptic curve over K. Essentially,our P-minimal conjectures hold in these contexts and, moreover,our case study of elliptic curves yields counterexamples toa more naive direct translation of the o-minimal conjectures.