Bifundamental representation
Encyclopedia
In mathematics
and theoretical physics
, a bifundamental representation is a representation
obtained as a tensor product
of two fundamental
or antifundamental
representations.
For example, the MN-dimensional representation (M,N) of the group
is a bifundamental representation.
These representations occur in quiver diagram
s.
Category:Abstract algebra
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, a bifundamental representation is a representation
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 studiesmodules over these abstract algebraic structures...
obtained as a tensor product
Tensor product
In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects. In each case the significance of the symbol is the same: the most general...
of two fundamental
Fundamental representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group...
or antifundamental
Antifundamental representation
In mathematics, an antifundamental representation is the complex conjugate of the fundamental representation, although the distinction between the fundamental and the antifundamental representation is a matter of convention. However, these two are often non-equivalent, because each of them is a...
representations.
For example, the MN-dimensional representation (M,N) of the group
is a bifundamental representation.
These representations occur in quiver diagram
Quiver diagram
In physics, a quiver diagram is a graph representing the matter content of a gauge theory that describes D-branes on orbifolds.Each node of the graph corresponds to a factor U of the gauge group, and each link represents a field in the bifundamental representation.The relevance of quiver diagrams...
s.
Category:Abstract algebra