scholarly journals Unitary principal series of split orthogonal groups

2014 ◽  
Vol 271 (2) ◽  
pp. 479-510
Author(s):  
Alessandra Pantano ◽  
Annegret Paul ◽  
Susana Riba
Keyword(s):  
Principal Series ◽  
Orthogonal Groups ◽  
Unitary Principal Series

scholarly journals Branching laws for small unitary representations of GL(n, ℂ)

2014 ◽  
Vol 25 (06) ◽  
pp. 1450052
Author(s):  
Jan Möllers ◽  
Benjamin Schwarz
Keyword(s):  
Parabolic Subgroup ◽  
Principal Series ◽  
Unitary Representations ◽  
Symmetric Pair ◽  
Maximal Parabolic Subgroup ◽  
Infinite Dimensional ◽  
Branching Laws ◽  
Series Representations ◽  
Unitary Principal Series ◽  
Kirillov Dimension

The unitary principal series representations of G = GL (n, ℂ) induced from a character of the maximal parabolic subgroup P = ( GL (1, ℂ) × GL (n - 1, ℂ)) ⋉ ℂn-1 attain the minimal Gelfand–Kirillov dimension among all infinite-dimensional unitary representations of G. We find the explicit branching laws for the restriction of these representations to all reductive subgroups H of G such that (G, H) forms a symmetric pair.

scholarly journals Spherical Unitary Principal Series

2005 ◽  
Vol 1 (4) ◽  
pp. 755-789 ◽  
Author(s):  
Dan Barbasch ◽  
Dan Ciubotaru
Keyword(s):  
Principal Series ◽  
Unitary Principal Series
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