On the Proof of the Capelli Identities

DOI10.1619/fesi.51.1zbMath1195.17009OpenAlexW2025097871MaRDI QIDQ3535818

Tôru Umeda

Publication date: 14 November 2008

Published in: Funkcialaj Ekvacioj (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1619/fesi.51.1

zbMATH Keywords

Capelli identityGrassmann algebracenter of universal enveloping algebranoncommutative determinants

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Vector and tensor algebra, theory of invariants (15A72) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Actions of groups on commutative rings; invariant theory (13A50)

Related Items (7)

Quantum immanants, double Young–Capelli bitableaux and Schur shifted symmetric functions ⋮ Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U( gl ( n )) ⋮ Capelli elements of the group algebra ⋮ Capelli identities for reductive dual pairs ⋮ Study-type determinants and their properties ⋮ Young–Capelli bitableaux, Capelli immanants in U(gl(n)) and the Okounkov quantum immanants ⋮ Extensions of the Tensor Algebra and Their Applications

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