Principal specializations of the classical groups and \(q\)-analogs of the dimension formulas

DOI10.1006/aima.1997.1606zbMath0867.22013OpenAlexW1976950475MaRDI QIDQ675874

Kazuhiko Koike

Publication date: 6 May 1997

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1997.1606

zbMATH Keywords

Young diagramclassical groupsirreducible representationsspinor group\(q\)-analogshook determinant formula

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Applications of Lie groups to the sciences; explicit representations (22E70) Semisimple Lie groups and their representations (22E46)

Related Items

Representations of spinor groups and the difference characters of \(SO(2n)\), A \(q\)-Brauer algebra, INVARIANT TENSORS AND DIAGRAMS, \(q\)-centralizer algebras for spin groups

Cites Work

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• Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
• Quantum groups and subfactors of type B, C, and D
• Tensor products of quantized tilting modules
• Poincaré series on symmetric and alternating tensors for irreducible representations of imprimitive complex reflection groups
• Representations of spinor groups and the difference characters of \(SO(2n)\)
• Dimensions of irreducible representations of the classical Lie groups