Abstract
Original language | English |
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Pages (from-to) | 87-105 |
Number of pages | 19 |
Journal | Monatshefte für Mathematik |
Volume | 176 |
Issue number | 1 |
Early online date | 17 Sep 2014 |
DOIs | |
Publication status | Published - Jan 2015 |
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Degenerate Principal series representations of SOo(p,p+1). / Fischer, Veronique; Zhang, Genkai.
In: Monatshefte für Mathematik, Vol. 176, No. 1, 01.2015, p. 87-105.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Degenerate Principal series representations of SOo(p,p+1).
AU - Fischer, Veronique
AU - Zhang, Genkai
PY - 2015/1
Y1 - 2015/1
N2 - For \(p\) odd, the Lie group \(G^\sharp =\mathrm{SO}_0(p+1,p+1)\) has a family of complementary series representations realized on the space of real \((p+1)\times (p+1)\) skew symmetric matrices, similar to the Stein’s complementary series for \(\mathrm{SL}(2n, {\mathbb C})\). We consider their restriction on the subgroup \(G_0=\mathrm{SO}_0(p+1,p)\) and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of \(G=\mathrm{SO}(p+1, p)\), and also irreducible under a maximal parabolic subgroup of \(G\).
AB - For \(p\) odd, the Lie group \(G^\sharp =\mathrm{SO}_0(p+1,p+1)\) has a family of complementary series representations realized on the space of real \((p+1)\times (p+1)\) skew symmetric matrices, similar to the Stein’s complementary series for \(\mathrm{SL}(2n, {\mathbb C})\). We consider their restriction on the subgroup \(G_0=\mathrm{SO}_0(p+1,p)\) and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of \(G=\mathrm{SO}(p+1, p)\), and also irreducible under a maximal parabolic subgroup of \(G\).
UR - http://dx.doi.org/10.1007/s00605-014-0671-x
U2 - 10.1007/s00605-014-0671-x
DO - 10.1007/s00605-014-0671-x
M3 - Article
VL - 176
SP - 87
EP - 105
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
SN - 0026-9255
IS - 1
ER -