In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a...

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of...

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra...

In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple...

In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple...

fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will assume all groups...

In representation theory, a branch of mathematics, the theorem of the highest weight classifies the irreducible representations of a complex semisimple...

Unitary representation Weight (representation theory) Peter–Weyl theorem Borel–Weil theorem Kirillov character formula Representation theory of SU(2)...

the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory was...

this highest weight. An important aspect of the representation theory is the associated theory of characters. Here, for a representation Σ {\displaystyle...

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or...

{\displaystyle k} -space. These weights – in particularly their geometry – are of central importance in understanding the representation theory of Lie algebras, specifically...

Fundamental representation Antifundamental representation Bifundamental representation Adjoint representation Weight (representation theory) Cartan's theorem...

refer to: Weight (graph theory) a number associated to an edge or to a vertex of a graph Weight (representation theory), a type of function Weight (strings)...

In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element...

connections between those areas. Graph theory plays an important role in electrical modeling of electrical networks, here, weights are associated with resistance...

In group theory, restriction forms a representation of a subgroup using a known representation of the whole group. Restriction is a fundamental construction...

This is a glossary of representation theory in mathematics. The term "module" is often used synonymously for a representation; for the module-theoretic...

In mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group...

representation theory of compact Lie groups), the weights of the dual representation are the negatives of the weights of the original representation....

the Lorentz group is deduced using the general framework of the representation theory of semisimple Lie algebras. The finite-dimensional representations...

In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations...

mathematics, weight space may refer to: Weight space (representation theory) Parameter space in artificial neural networks, where the parameters are weights on...

mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained...

to Hamming weight in the binary case, in 1954. Hamming weight is used in several disciplines including information theory, coding theory, and cryptography...

Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and...

In mathematics, a source for the representation theory of the group of diffeomorphisms of a smooth manifold M is the initial observation that (for M connected)...

)}} and each weight space is one-dimensional. Elements of S are called Dirac spinors. When n is even, S is not an irreducible representation: S + = ∧ e...

In the mathematical field of representation theory, a Kazhdan–Lusztig polynomial P y , w ( q ) {\displaystyle P_{y,w}(q)} is a member of a family of integral...

irreducible unitary representations of G: the highest weight representation L(λ) with highest weight λ∈h*+ corresponds to the integral coadjoint orbit G·λ...