On duality and negative dimensions in the theory of Lie groups and symmetric spaces

DOI10.1063/1.3625954zbMath1272.53045arXiv1011.0151OpenAlexW3105990877WikidataQ115333373 ScholiaQ115333373MaRDI QIDQ2849732

R. L. Mkrtchyan, Alexander P. Veselov

Publication date: 24 September 2013

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

Full work available at URL: https://arxiv.org/abs/1011.0151

zbMATH Keywords

Jack and Jacobi symmetric functionsMacdonald duality

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) General properties and structure of complex Lie groups (22E10) Complex Lie groups, group actions on complex spaces (32M05) Differential geometry of symmetric spaces (53C35) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items (13)

Commutators of random matrices from the unitary and orthogonal groups ⋮ Universal volume of groups and anomaly of Vogel's symmetry ⋮ Higher spin realization of the DS/CFT correspondence ⋮ Duality of orthogonal and symplectic random tensor models: general invariants ⋮ Duality of O(N) and Sp(N) random tensor models: tensors with symmetries ⋮ Matrix group integrals, surfaces, and mapping class groups. II: \( \mathrm{O}\left( n\right)\) and \(\mathrm{Sp}\left( n\right) \) ⋮ On the road map of Vogel's plane ⋮ Minimal model holography for SO(2\(N\)) ⋮ On (ad)n(X2)k series of universal quantum dimensions ⋮ Universality in Chern-Simons theory ⋮ Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters ⋮ Casimir eigenvalues for universal Lie algebra ⋮ X ₂ series of universal quantum dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(BC_\infty \) Calogero-Moser operator and super Jacobi polynomials
• Quantum systems related to root systems, and radial parts of Laplace operators
• Duality of orthogonal and symplectic matrix integrals and quaternionic Feynman graphs
• Some combinatorial properties of Jack symmetric functions
• A universal dimension formula for complex simple Lie algebras
• Universal characters from the MacDonald identities
• Jack, Hall-Littlewood and Macdonald Polynomials
• Spinors in Negative Dimensions
• S Theorem and Construction of the Invariants of the Semisimple Compact Lie Algebras
• CASIMIR OPERATORS FOR SEMISIMPLE LIE GROUPS
• The Dimensions of Irreducible Tensor Representations of the Orthogonal and Symplectic Groups

This page was built for publication: On duality and negative dimensions in the theory of Lie groups and symmetric spaces