especially in the field of representation theory, Schur functors (named after Issai Schur) are certain functors from the category of modules over a fixed commutative...

↦ S λ ( V ) {\displaystyle V\mapsto S^{\lambda }(V)} is a functor called the Schur functor. It generalizes the constructions of symmetric and exterior...

orthogonal group. k-Schur functions Grothendieck polynomials (K-theoretical analogue of Schur polynomials) LLT polynomials Schur functor Littlewood–Richardson...

complement method Schur complement Schur-convex function Schur decomposition Schur functor Schur index Schur's inequality Schur's lemma (from Riemannian...

In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H 2 ( G , Z ) {\displaystyle H_{2}(G,\mathbb {Z}...

are polynomial functors from V {\displaystyle {\mathcal {V}}} to V {\displaystyle {\mathcal {V}}} ; these two are also Schur functors. The notion appears...

the general linear group GL(V). Each Young diagram λ corresponds to a Schur functor Lλ(-) on the category of GL(V)-representations. Given two Young diagrams...

Alternating polynomials Symmetric polynomials Schur functor Robinson–Schensted correspondence Schur–Weyl duality Jucys–Murphy element Garnir relations...

non-isomorphic irreducible representations are orthogonal to each other. 4.  The Schur functor V ↦ S λ ( V ) {\displaystyle V\mapsto S^{\lambda }(V)} constructs representations...

→ Hom(F(V), F(W)) is a polynomial map between the vector spaces. A Schur functor is a basic example. pre-abelian A pre-abelian category is an additive...

also called tensor representations, and can be obtained by applying Schur functors (associated to Young tableaux). These coincide with the rational representations...

convention). Then each S {\displaystyle \mathbb {S} } -module determines a Schur functor on V e c t {\displaystyle {\mathsf {Vect}}} . This definition of S {\displaystyle...

of the symmetric group plays a fundamental role through the ideas of Schur functors. In the theory of Coxeter groups, the symmetric group is the Coxeter...

signalizer functor is a mapping from a potential finite subgroup to the centralizers of the nontrivial elements of an abelian group. The signalizer functor theorem...

representation theory, the exterior algebra is one of the two fundamental Schur functors on the category of vector spaces, the other being the symmetric algebra...

C {\displaystyle A\to \mathbb {C} } (described in detail in the article Schur orthogonality relations). Now, for any class functions ψ : H → C {\displaystyle...

replaces sets with categories, functions with functors, and equations with natural isomorphisms of functors satisfying additional properties. The term was...

in positive characteristic. The divided power functor is used in the construction of co-Schur functors. Crystalline cohomology The uniqueness follows...

powers. Both expressions are subsumed in expressions of Schur polynomials as traces over Schur functors, which can be seen as the Weyl character formula for...

category C, a representation of G in the category C is a functor from G to C. Such a functor selects an object of C and a subgroup of automorphisms of...

{\displaystyle V_{\lambda _{1},\dots ,\lambda _{n}}} in terms of a Schur functor. The dimension of V λ μ {\displaystyle V_{\lambda \mu }} where λ = (...

commonly referred to simply as semidirect products. For finite groups, the Schur–Zassenhaus theorem provides a sufficient condition for the existence of...

D-modules. Akin, Kaan; Buchsbaum, David A.; Weyman, Jerzy (1982). "Schur Functors and Schur Complexes" (PDF). Advances in Mathematics. 44 (3): 207–278. doi:10...

is then nothing but a (covariant) functor from G to the category of sets, and a group representation is a functor from G to the category of vector spaces...

{\displaystyle M^{G}} yields a functor from the category of G-modules to the category Ab of abelian groups. This functor is left exact but not necessarily...

simple groups. The Schreier conjecture The Signalizer functor theorem The B conjecture The Schur–Zassenhaus theorem for all groups (though this only uses...

vector spaces Homological algebra Filtration (algebra) Exact sequence Functor Zorn's lemma Semigroup Subsemigroup Free semigroup Green's relations Inverse...

for measurable spaces (measure theory) Schur's lemma (representation theory) Schur's theorem (Ramsey theory) Schur–Zassenhaus theorem (group theory) Schwartz...

and inverse axioms) a functor from schemes over S to the category of groups, such that composition with the forgetful functor to sets is equivalent to...

simple module is a division ring. This result is known as Schur's lemma. The converse of Schur's lemma is not true in general. For example, the Z-module...