scholarly journals Capelli identity and relative discrete series of line bundles over tube domains

2002 ◽  
Vol 55 ◽  
pp. 349-357 ◽  
Author(s):  
Bent Ørsted ◽  
Genkai Zhang
Keyword(s):  
Discrete Series ◽  
Line Bundles ◽  
Tube Domains ◽  
Capelli Identity

scholarly journals Relative discrete series of line bundles over bounded symmetric domains

1996 ◽  
Vol 46 (4) ◽  
pp. 1011-1026 ◽  
Author(s):  
Anthony H. Dooley ◽  
Bent Ørsted ◽  
Genkai Zhang
Keyword(s):  
Discrete Series ◽  
Line Bundles ◽  
Bounded Symmetric Domains

scholarly journals TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS

2008 ◽  
Vol 19 (10) ◽  
pp. 1247-1268 ◽  
Author(s):  
HENRIK SEPPÄNEN
Keyword(s):  
Discrete Series ◽  
Intertwining Operators ◽  
Plancherel Measure ◽  
Minimal Representation ◽  
Holomorphic Discrete Series ◽  
Absolutely Continuous ◽  
Tube Domains ◽  
Rank One ◽  
Minimal Representations

In this paper, we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from Sp(n, ℝ) to GL+(n, ℝ), and from SU(n, n) to GL(n, ℂ) respectively. We work with the realizations of the representation spaces as L2-spaces on the boundary orbits of rank one of the corresponding cones, and give explicit integral operators that play the role of the intertwining operators for the decomposition. We prove inversion formulas for dense subspaces and use them to prove the Plancherel theorem for the respective decomposition. The Plancherel measure turns out to be absolutely continuous with respect to the Lebesgue measure in both cases.

Hard Objects in George Oppen's Discrete Series

2018 ◽  
Vol 13 (4) ◽  
pp. 496-517
Author(s):  
Ned Hercock
Keyword(s):  
Twentieth Century ◽  
Ludwig Wittgenstein ◽  
Discrete Series ◽  
Human Experience ◽  
John Ruskin ◽  
Gerard Manley Hopkins ◽  
Marcel Duchamp ◽  
The World ◽  
Production History ◽  
History Of

This essay examines the objects in George Oppen's Discrete Series (1934). It considers their primary property to be their hardness – many of them have distinctively uniform and impenetrable surfaces. This hardness and uniformity is contrasted with 19th century organicism (Gerard Manley Hopkins and John Ruskin). Taking my cue from Kirsten Blythe Painter I show how in their work with hard objects these poems participate within a wider cultural and philosophical turn towards hardness in the early twentieth century (Marcel Duchamp, Adolf Loos, Ludwig Wittgenstein and others). I describe the thinking these poems do with regard to industrialization and to human experience of a resolutely object world – I argue that the presentation of these objects bears witness to the production history of the type of objects which in this era are becoming preponderant in parts of the world. Finally, I suggest that the objects’ impenetrability offers a kind of anti-aesthetic relief: perception without conception. If ‘philosophy recognizes the Concept in everything’ it is still possible, these poems show, to experience resistance to this imperious process of conceptualization. Within thinking objects (poems) these are objects which do not think.

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