scholarly journals Radon Transform: Dual Pairs and Irreducible Representations

2020 ◽  
pp. 1-28
Author(s):  
Giovanni S. Alberti ◽  
Francesca Bartolucci ◽  
Filippo De Mari ◽  
Ernesto De Vito
Keyword(s):  
Radon Transform ◽  
Irreducible Representations ◽  
Dual Pairs

scholarly journals Unitarization and Inversion Formulae for the Radon Transform Between Dual Pairs

2019 ◽  
Vol 51 (6) ◽  
pp. 4356-4381 ◽  
Author(s):  
Giovanni S. Alberti ◽  
Francesca Bartolucci ◽  
Filippo De Mari ◽  
Ernesto De Vito
Keyword(s):  
Radon Transform ◽  
Dual Pairs ◽  
And Inversion

scholarly journals Dual pair correspondence in physics: oscillator realizations and representations

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Thomas Basile ◽  
Euihun Joung ◽  
Karapet Mkrtchyan ◽  
Matin Mojaza
Keyword(s):  
Closed Form ◽  
Fock Space ◽  
Dual Pair ◽  
Irreducible Representations ◽  
Systematic Treatment ◽  
Dual Pairs ◽  
Howe Duality ◽  
Casimir Operators ◽  
General Aspects ◽  
Dual Pair Correspondence

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.

An Intuitive Method for the Determination of Crystal-Field Parameters in Laser Crystals

1993 ◽  
Vol 329 ◽  
Author(s):  
Frederick G. Anderson ◽  
H. Weidner ◽  
P. L. Summers ◽  
R. E. Peale ◽  
B. H. T. Chai
Keyword(s):  
Crystal Field ◽  
Irreducible Representations ◽  
Laser Crystals ◽  
Intuitive Method ◽  
Crystal Field Parameters ◽  
Intuitive Interpretation

AbstractExpanding the crystal field in terms of operators that transform as the irreducible representations of the Td group leads to an intuitive interpretation of the crystal-field parameters. We apply this method to the crystal field experienced by Nd3+ dopants in the laser crystals YLiF4, YVO4, and KLiYF5.

The Modulo Radon Transform and its Inversion

2021 ◽  
Author(s):  
Ayush Bhandari ◽  
Matthias Beckmann ◽  
Felix Krahmer
Keyword(s):  
Radon Transform
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