# Representation theory

2017-07-30T19:03:59+03:00[Europe/Moscow] en true Young tableau, Semisimple module, Representation theory, Group representation, Clebsch–Gordan coefficients, Restricted representation, Zoghman Mebkhout, Irreducible representation, Crystal base, Freudenthal magic square, Oscillator representation, Projective representation, List of representation theory topics, Schubert variety flashcards Representation theory
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• Young tableau
In mathematics, a Young tableau (pl.: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.
• Semisimple module
In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts.
• 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.
• 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 operation can be represented by matrix multiplication.
• Clebsch–Gordan coefficients
In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics.
• Restricted representation
In mathematics, restriction is a fundamental construction in representation theory of groups.
• Zoghman Mebkhout
Zoghman Mebkhout (born 1949 ) (مبخوت زغمان) is an Algerian mathematician known for his work in algebraic analysis, geometry, and representation theory, more precisely on the theory of D-modules.
• Irreducible representation
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper subrepresentation closed under the action of .
• Crystal base
In algebra, a crystal base or canonical base is a base of a representation, such that generators of a quantum group or semisimple Lie algebra have a particularly simple action on it.
• Freudenthal magic square
In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups).
• Oscillator representation
In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David Shale, and André Weil.
• Projective representation
In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group PGL(V, F) = GL(V, F) / F∗, where GL(V, F) is the general linear group of invertible linear transformations of V over F and F∗ is the normal subgroup consisting of multiplications of vectors in V by nonzero elements of F (that is, scalar multiples of the identity; scalar transformations).
• List of representation theory topics