What is a representation in representation theory?
What is a representation in representation theory?
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. Representation theory is pervasive across fields of mathematics for two reasons.
Who discovered representation theory?
Abstract. Representation theory was created by Frobenius about 100 years ago. We describe the background that led to the problem which motivated Frobenius to define characters of a finite group and show how representation theory solves the problem.
Why is the Langlands program so important?
As an analogue to the possible exact distribution of primes, the Langlands program allows a potential general tool for resolution of invariance at generalized algebraic structures. This in turn permits a somewhat unified analysis of arithmetic objects through their automorphic functions.
What is representation analysis?
Representation always involves a certain degree of abstraction—that is, the taking away of one characteristic or more of the original. The representation is, of course, not a visual one; it is representation through language. …
What are the different types of representations?
Models of representation refer to ways in which elected officials behave in representative democracies. There are three main types: delegate, trustee, and politico.
What is an infinite dimensional representation of a group?
Infinite-dimensional representation. A representation of a Lie group (cf. Representation of a topological group) in an infinite-dimensional vector space. The theory of representations of Lie groups is part of the general theory of representations of topological groups.
What is a representation of a Lie group?
A representation of a Lie group (cf. Representation of a topological group) in an infinite-dimensional vector space. The theory of representations of Lie groups is part of the general theory of representations of topological groups.
What is representrepresentation theory?
Representation theory reverses the question to “Given a group G, what objects X does it act on?” and attempts to answer this question by classifying such Xup to isomorphism. Before restricting to the linear case, our main concern, let us remember another way to describe an action of Gon X.
What is the general theory of non-unitary representations?
The general theory of non-unitary representations in locally convex vector spaces, which began to develop in the 1950’s, is based to a great extent on the theory of topological vector spaces and on the theory of generalized functions.
