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Schur polynomial

In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear…

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Overview

Definition (Jacobi's bialternant formula)

Properties

Example

Relation to representation theory

Schur positivity

Generalizations

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Map overview Semantic statistics

Schur polynomial

Nodes52
Edges51
Triples70
Avg. degree1.96
Density0.038462
Components1

How this topic connects Entity context

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Schur polynomial

Top relations

related to Other generalizations · 10
Schur polynomial → Demazure, Hall, K-theoretical, Key, Littlewood, LLT, Quasi-symmetric Schur, Schubert, Schur, There
related to Double Schur polynomials · 9
Schur polynomial → Given, Here, In, Littlewood-Richardson, Molev, Schur, The, These, Young
related to Properties · 9
Schur polynomial → For, Gessel, Giambelli, Lindström, Schur, The, This, Viennot, Young
related to Specializations · 9
Schur polynomial → Evaluating, Hook, In, One, Schur, See, The, Weyl, Young
related to Factorial Schur polynomials · 7
Schur polynomial → Given, Here, It, Schur, The, There, Young
related to Relation to representation theory · 7
Schur polynomial → If, Lie, Schur, Schur's, Several, The Schur, The Weyl
related to Jacobi−Trudi identities · 4
Schur polynomial → Jacobi, Schur, The, Trudi
related to Skew Schur functions · 4
Schur polynomial → Hall, Here, Schur, Skew Schur
related to Further identities · 3
Schur polynomial → Hall, Littlewood, The Schur
related to The Murnaghan−Nakayama rule · 3
Schur polynomial → Nakayama, Schur, The Murnaghan

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Important terminology

schur polynomials symmetric displaystyle functions partitions polynomial formula lambda linear rule determinant partition sum young variables given also littlewood skew

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Schur polynomialis asum of monomials0.90text
Schur polynomialrelated to Definition (Jacobi's bialternant formula)Schur0.60section
Schur polynomialrelated to Definition (Jacobi's bialternant formula)Given0.60section
Schur polynomialrelated to Double Schur polynomialsThe0.60section
Schur polynomialrelated to Double Schur polynomialsSchur0.60section
Schur polynomialrelated to Double Schur polynomialsThese0.60section
Schur polynomialrelated to Double Schur polynomialsGiven0.60section
Schur polynomialrelated to Double Schur polynomialsYoung0.60section
Schur polynomialrelated to Double Schur polynomialsHere0.60section
Schur polynomialrelated to Double Schur polynomialsLittlewood-Richardson0.60section
Schur polynomialrelated to Double Schur polynomialsMolev0.60section
Schur polynomialrelated to Double Schur polynomialsIn0.60section

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