Author:
Basile Thomas,Joung Euihun,Mkrtchyan Karapet,Mojaza Matin
Abstract
Abstract
We study general aspects of the reductive dual pair correspondence, also known as Howe duality. We make an explicit and systematic treatment, where we first derive the oscillator realizations of all irreducible dual pairs: (GL(M, ℝ), GL(N, ℝ)), (GL(M, ℂ), GL(N, ℂ)), (U∗(2M), U∗(2N)), (U (M+, M−), U (N+, N−)), (O(N+, N−), Sp (2M, ℝ)), (O(N, ℂ), Sp(2M, ℂ)) and (O∗(2N ), Sp(M+, M−)). Then, we decompose the Fock space into irreducible representations of each group in the dual pairs for the cases where one member of the pair is compact as well as the first non-trivial cases of where it is non-compact. We discuss the relevance of these representations in several physical applications throughout this analysis. In particular, we discuss peculiarities of their branching properties. Finally, closed-form expressions relating all Casimir operators of two groups in a pair are established.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Cited by
5 articles.
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