Invariant Theory of the Dual Pairs (SO ∗ (2n), Sp(2k, \mathabfC)) and (Sp(2n, \mathfracR), O(N))

DOI10.2307/2160166zbMATH Open0796.22006OpenAlexW2051798579MaRDI QIDQ4281736

Eric Y. Leung, T. Ton-That

Publication date: 29 August 1994

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2160166

zbMATH Keywords

differential operatorsuniversal enveloping algebrapolynomial invariantsadjoint representationCasimir operatorsdual pairsset of generators

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Lie algebras of Lie groups (22E60) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

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The explicit duality correspondence of (\(\text{Sp}(p,q),\text{O}^{*}(2n)\)) ⋮ Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\) ⋮ On the unitary dual of 𝑆𝑝𝑖𝑛(2𝑛,ℂ)

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