WebChapter II]). In this instance, Howe’s treatment of dual pairs in certain Lie algebras gives rise to a classi cation of the dual pairs in Sp(2n;C). However, it is not, in general, the case that the dual pairs in an algebraic group Gcan be understood by looking at the dual pairs in the Lie algebra associated to G. Web@article{RogerHowe2010, abstract = {We propose a generalization of the theory of spherical harmonics to the context of symmetric subgroups of reductive groups acting on …

Examples of dual reductive pairs Semantic Scholar

Web1 mrt. 1999 · DOI: 10.1016/S0393-0440(98)00043-6 Corpus ID: 120933010; Classification and partial ordering of reductive Howe dual pairs of classical Lie groups @article{Schmidt1999ClassificationAP, title={Classification and partial ordering of reductive Howe dual pairs of classical Lie groups}, author={Matthias Schmidt}, journal={Journal of … Web16 okt. 2024 · Dual pairs in complex reductive groups Marisa Gaetz In Roger Howe's 1989 paper, "Remarks on classical invariant theory," Howe introduces the notion of a "dual pair of Lie subalgebras" - a pair of reductive Lie subalgebras of a Lie algebra such that and are each other's centralizers in . fish on hilton head

(PDF) The Howe dual pair in Hermitean Clifford analysis

A reductive dual pair is called reducible if it can be obtained in this fashion from smaller groups, and irreducible otherwise. A reducible pair can be decomposed into a direct product of irreducible ones, and for many purposes, it is enough to restrict one's attention to the irreducible case. Meer weergeven In the mathematical field of representation theory, a reductive dual pair is a pair of subgroups (G, G′) of the isometry group Sp(W) of a symplectic vector space W, such that G is the centralizer of G′ in Sp(W) and vice … Meer weergeven The notion of a reductive dual pair makes sense over any field F, which we assume to be fixed throughout. Thus W is a symplectic vector space over F. If W1 and W2 are two symplectic vector spaces and (G1, G′1), (G2, G′2) are two reductive … Meer weergeven • The full symplectic group G = Sp(W) and the two-element group G′, the center of Sp(W), form a reductive dual pair. The double centralizer property is clear from the way these groups were defined: the centralizer of the group G in G is its center, and … Meer weergeven • Howe correspondence between representations of elements of a reductive dual pair. • Heisenberg group Meer weergeven Web20 okt. 2024 · During the Howe conference, the first author presented his paper with S. Takeda on the proof of the Howe duality conjecture for orthogonal-symplectic and unitary … Web1 mrt. 1999 · Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup. A bstract . In this paper, we obtain a full classification … fish on hockey ice