Schur 𝑄-functions and the Capelli eigenvalue problem for the Lie superalgebra \ger𝑞(𝑛)

DOI10.1090/conm/714/14376zbMath1452.17010arXiv1701.03401OpenAlexW3106292148MaRDI QIDQ4961920

Hadi Salmasian, Alexander Alldridge, Siddhartha Sahi

Publication date: 29 October 2018

Published in: Representation Theory and Harmonic Analysis on Symmetric Spaces (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.03401

zbMATH Keywords

Capelli identityqueer Lie superalgebraSchur \(Q\)-function

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (5)

Linear transformations of vertex operators of Hall-Littlewood polynomials ⋮ Spherical indecomposable representations of Lie superalgebras ⋮ Unnamed Item ⋮ The Capelli eigenvalue problem for Lie superalgebras ⋮ Multiparameter Schur \(Q\)-functions are solutions of the BKP hierarchy

Cites Work

• The Capelli problem for \(\mathfrak{gl}(m|n)\) and the spectrum of invariant differential operators
• The centre of enveloping algebra for Lie superalgebra Q(n,\({\mathbb{C}})\)
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Shifted tableaux and the projective representations of symmetric groups
• The theory of Lie superalgebras. An introduction
• Jordan algebras and Capelli identities
• Remarks on the Schur-Howe-Sergeev duality
• Generalised discriminants, deformed Calogero-Moser-Sutherland operators and super-Jack polynomials
• The Capelli identity, tube domains, and the generalized Laplace transform
• Dimensions of skew-shifted Young diagrams and projective characters of the infinite symmetric group
• Mathematical foundations of supersymmetry
• The Capelli eigenvalue problem for Lie superalgebras
• Spherical representations of Lie supergroups
• Capelli identities for lie superalgebras
• SUPERORBITS
• Jordan algebras and degenerate principal series.
• Lie superalgebras
• Combinatorial formula for factorial Schur \(Q\)-functions
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