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representation theory

   Also found in: Wikipedia 0.01 sec.
representation theory [‚rep·ri‚zen′tā·shən ‚thē·ə·rē]
(mathematics)
The study of groups by the use of their representations.
The determination of representations of specific groups.
(quantum mechanics)
Quantum-mechanical device in which one selects the common eigenfunctions of a complete set of quantum-mechanical operators as a basis of vectors in a Hilbert space, and expresses wave functions and operators in terms of column matrices and square matrices, respectively, which correspond to this basis.


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The authors explore the need for quantum mechanics and its physical basis to discuss representation theory, equations of motion, bound states of simple systems, symmetries and conservation laws, angular momentum, approximation methods, the three-body problem and quantization of radiation fields.
Despite the difficulty of his subject matter - he teaches abstract algebra and algebraic representation theory - students praise Brundan's sense of humor and ability to cut through complex problems.
The introduction, written by Helgason, provides background on the subjects of the articles: invariant differential operators, geometric properties of solutions, double fibrations in integral geometry, Radon transforms, spherical functions and transforms, duality for symmetric spaces, representation theory, Fourier transform on Riemannian symmetric spaces, and multipliers.
 
 
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