ar X iv : 0 90 3 . 28 70 v 1 [ cs . L G ] 1 6 M ar 2 00 9 ON p - ADIC CLASSIFICATION

ar X iv : m at h - ph / 0 30 30 45 v 1 1 9 M ar 2 00 3 p – Adic pseudodifferential operators and p – adic wavelets

We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators.

ar X iv : 0 81 2 . 38 70 v 1 [ m at h . R T ] 1 9 D ec 2 00 8 DEPTH ZERO REPRESENTATIONS OF NONLINEAR COVERS OF p - ADIC GROUPS

We generalize the methods of Moy-Prasad, in order to define and study the genuine depth zero representations of some nonlinear covers of reductive groups over p-adic local fields. In particular, we construct all depth zero supercuspidal representations of the metaplectic group Mp2n over a p-adic field of odd residue characteristic.

ar X iv : 0 90 8 . 33 40 v 1 [ m at h . R T ] 2 3 A ug 2 00 9 DICHOTOMY FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF G

The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3 when p 6= 2. This ...

ar X iv : 0 90 3 . 05 62 v 1 [ as tr o - ph . G A ] 3 M ar 2 00 9 Introduction to Millimeter / Sub - Millimeter

ar X iv : m at h - ph / 0 30 60 23 v 1 9 J un 2 00 3 Non - Archimedean Geometry and Physics on

This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.