p-adic representation

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• Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

• p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …   Wikipedia

• P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

• p-adic Hodge theory — In mathematics, p adic Hodge theory is a theory that provides a way to classify and study p adic Galois representations of characteristic 0 local fields[1] with residual characteristic p (such as Qp). The theory has its beginnings in Jean Pierre… …   Wikipedia

• P-adic quantum mechanics — One may compute the energy levels for a potential well like this one.[note 1] P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p adic analysis to quantum… …   Wikipedia

• Admissible representation — In mathematics, admissible representations are a well behaved class of representations used in the representation theory of reductive Lie groups over real or p adic fields. They were introduced by Harish Chandra.Real reductive groupsFor real… …   Wikipedia

• Tempered representation — In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the L p space : L 2+ epsilon;( G ) for any epsilon; gt; 0. FormulationThis condition, as just given,… …   Wikipedia

• Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

• Principal series representation — In mathematics, the principal series representations of certain kinds of topological group G occur in the case where G is not a compact group. There, by analogy with spectral theory, one expects that the regular representation of G will decompose …   Wikipedia

• Unipotent representation — In mathematics, a unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups. Informally, Langlands philosophy suggests that there should be a correspondence between… …   Wikipedia

• Complementary series representation — In mathematics, complementary series representations of a reductive real or p adic Lie groups are certain irreducible unitary representations that are not tempered and do not appear in the decomposition of the regular representation into… …   Wikipedia