On the matrix elements of the U(n) generators

DOI10.1063/1.524749zbMath0505.22019OpenAlexW2069099986WikidataQ60732506 ScholiaQ60732506MaRDI QIDQ4740755

Mark D. Gould

Publication date: 1981

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://espace.library.uq.edu.au/view/UQ:299744/UQ299744_OA.pdf

zbMATH Keywords

Wigner coefficientsalgebraic infinitesimal

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Compact groups (22C05)

Related Items (23)

Matrix elements of unitary group generators in many-fermion correlation problem. II: Graphical methods of spin algebras ⋮ Matrix elements of unitary group generators in many-fermion correlation problem. III. Green-Gould approach ⋮ Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras ⋮ Yangians and Gelfand-Zetlin bases ⋮ Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})$ revisited] ⋮ Casimir invariants and infinitesimal characters for semi-simple Lie algebras ⋮ Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n) ⋮ Valence bond approach and Verma bases ⋮ Multiplicity-free Wigner coefficients for semisimple Lie groups. I. The U(n) pattern calculus ⋮ Matrix elements and Wigner coefficients for U q[gl(n)] ⋮ Unnamed Item ⋮ Parastatistics and the Clifford algebra unitary group approach to the many-electron correlation problem ⋮ Reduced Wigner coefficients for Lie superalgebragl(m|n) corresponding to unitary representations and beyond ⋮ Unnamed Item ⋮ The Gel'fand-Tsetlin basis for irreducible unitarizable representations of u(p,q) with a highest weight ⋮ Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n) ⋮ Representation theory of the symplectic groups. I ⋮ Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n) ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ Cayley–Hamilton theorem for quantum matrix algebras of $GL(m|n)$ type ⋮ Gelfand-Tsetlin basis for representations of Yangians ⋮ A projection-based solution to the SP(2N) state labeling problem ⋮ Classification of simple Gelfand–Tsetlin modules of 𝔰𝔩(3)

Cites Work

• On an infinitesimal approach to semisimple Lie groups and raising and lowering operators of O(n) and U(n)
• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• On the Representations of the Semisimple Lie Groups. II

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