nLab reductive dual pair

Idea

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Related concepts

• reductive Lie algebra

References

The original articles:

• Roger Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989) 539-570 [doi:10.2307%2F2001418]

• Roger Howe, Transcending classical invariant theory, J. Amer. Math. Soc. 2 (1989) 535-552 [doi:10.2307%2F1990942]

See also:

• Wikipedia, Reductive dual pair

• M.J. Carvalho, J. Repka, D.J. Rowe, Simple unified proofs of four duality theorems, J. Math. Phys. 52 (2011) 013507 [DOI:10.1063/1.3525978]

• M.J. Carvalho, J. Repka, D.J. Rowe, Dual pairing of symmetry groups and dynamical groups in physics, Rev. Mod. Phys. 84 (2012) 711-757 [arXiv:1207.0148, DOI:10.1103/RevModPhys.84.711]

Generalization to super Lie algebras:

• Allan Merino, Hadi Salmasian, Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup [arXiv:2208.09746]

• Shun-Jen Cheng, Weiqiang Wang, Dualities and representations of Lie superalgebras, Graduate Studies in Mathematics 144 American Mathematical Society 2012, [doi:10.1090/gsm/144]

Analogues of Howe dual pairs in vertex operator algebra theory

• B. Lian, Andrew Linshaw, Howe pairs in the theory of vertex algebras, J. Algebra 317 (2007) 111-152 arXiv:math.RT/0605174 doi