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On the nondegenerate complementary series of representations of the groupSU 2,2

О невырожденных дополнительных рядах представлений группыSU 2.2

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

Two series of unitary irreducible representations of the non-degenerate complementary series ofSU 2.2 are constructed. They are closely related to the first and second principal series of representations. We also examine a third series of irreducible representations, akin to the zeroth (discrete) principal series; an invariant Hermitian functional is presented, but we have been unable to determine its positivity, and hence the unitarity of the representation.

Riassunto

Si costruiscono due serie di rappresentazioni unitarie irriducibili della serie complementare non degenere diSU 2.2. Esse sono in stretta relazione con la prima e la seconda serie principali di rappresentazioni. Si esamina anche una terza serie di rappresentazioni irriducibili, simile alla serie principale (discreta) di ordine zero, ma non si è potuto determinare la sua positività e quindi l'unitarietà della rappresentazione.

Резюме

Конструируются два ряда унитарных неприводимых представлений для невырожденных дополнительных рядов группыSU 2,2. Эти ряды тесно связаны с первым и вторым основными рядами представлений. Мы также исследуем третий ряд неприводимых представлений, похожий на нулевой (дискретный) основной ряд. Приводится инвариантный эрмитов функционал, но мы не можем определить его положительность и, следовательно, унитарность этого представления.

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References

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge

    N. W. Macfadyen

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  1. N. W. Macfadyen
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Traduzione a cura della Redazione.

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Macfadyen, N.W. On the nondegenerate complementary series of representations of the groupSU 2,2 . Nuov Cim A 10, 268–276 (1972). https://doi.org/10.1007/BF02895763

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  • DOI: https://doi.org/10.1007/BF02895763

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