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**Geometry of the Borel - de Siebenthal discrete series.** / Ørsted, Bent; Wolf, Joseph A.

Research output: Working paper/Preprint › Working paper › Research

Ørsted, B & Wolf, JA 2009 'Geometry of the Borel - de Siebenthal discrete series' Department of Mathematical Sciences, Aarhus University, Århus. <http://www.imf.au.dk/publs?id=696>

Ørsted, B., & Wolf, J. A. (2009). *Geometry of the Borel - de Siebenthal discrete series*. Department of Mathematical Sciences, Aarhus University. http://www.imf.au.dk/publs?id=696

Ørsted B, Wolf JA. 2009. Geometry of the Borel - de Siebenthal discrete series. Århus: Department of Mathematical Sciences, Aarhus University.

Ørsted, Bent and Joseph A Wolf *Geometry of the Borel - de Siebenthal discrete series*. Århus: Department of Mathematical Sciences, Aarhus University. 2009., 32 p.

Ørsted B, Wolf JA. Geometry of the Borel - de Siebenthal discrete series. Århus: Department of Mathematical Sciences, Aarhus University. 2009.

Ørsted, Bent ; Wolf, Joseph A. / **Geometry of the Borel - de Siebenthal discrete series**. Århus : Department of Mathematical Sciences, Aarhus University, 2009.

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title = "Geometry of the Borel - de Siebenthal discrete series",

abstract = "Let G0 be a connected, simply connected real simple Lie group. Suppose that G0 has a compact Cartan subgroup T0, so it has discrete series representations. Relative to T0 there is a distinguished positive root system + for which there is a unique noncompact simple root , the “Borel – de Siebenthal system”. There is a lot of fascinating geometry associated to the corresponding “Borel – de Siebenthal discrete series” representations of G0. In this paper we explore some of those geometric aspects and we work out the K0–spectra of the Borel – de Siebenthal discrete series representations. This has already been carried out in detail for the case where the associated symmetric space G0/K0 is of hermitian type, i.e. where has coefficient 1 in the maximal root μ, so we assume that the group G0 is not of hermitian type, in other words that has coefficient 2 in μ. Several authors have studied the case where G0/K0 is a quaternionic symmetric space and the inducing holomorphic vector bundle is a line bundle. That is the case where μ is orthogonal to the compact simple roots and the inducing representation is 1–dimensional.",

author = "Bent {\O}rsted and Wolf, {Joseph A}",

year = "2009",

language = "English",

publisher = "Department of Mathematical Sciences, Aarhus University",

address = "Denmark",

type = "WorkingPaper",

institution = "Department of Mathematical Sciences, Aarhus University",

}

TY - UNPB

T1 - Geometry of the Borel - de Siebenthal discrete series

AU - Ørsted, Bent

AU - Wolf, Joseph A

PY - 2009

Y1 - 2009

N2 - Let G0 be a connected, simply connected real simple Lie group. Suppose that G0 has a compact Cartan subgroup T0, so it has discrete series representations. Relative to T0 there is a distinguished positive root system + for which there is a unique noncompact simple root , the “Borel – de Siebenthal system”. There is a lot of fascinating geometry associated to the corresponding “Borel – de Siebenthal discrete series” representations of G0. In this paper we explore some of those geometric aspects and we work out the K0–spectra of the Borel – de Siebenthal discrete series representations. This has already been carried out in detail for the case where the associated symmetric space G0/K0 is of hermitian type, i.e. where has coefficient 1 in the maximal root μ, so we assume that the group G0 is not of hermitian type, in other words that has coefficient 2 in μ. Several authors have studied the case where G0/K0 is a quaternionic symmetric space and the inducing holomorphic vector bundle is a line bundle. That is the case where μ is orthogonal to the compact simple roots and the inducing representation is 1–dimensional.

AB - Let G0 be a connected, simply connected real simple Lie group. Suppose that G0 has a compact Cartan subgroup T0, so it has discrete series representations. Relative to T0 there is a distinguished positive root system + for which there is a unique noncompact simple root , the “Borel – de Siebenthal system”. There is a lot of fascinating geometry associated to the corresponding “Borel – de Siebenthal discrete series” representations of G0. In this paper we explore some of those geometric aspects and we work out the K0–spectra of the Borel – de Siebenthal discrete series representations. This has already been carried out in detail for the case where the associated symmetric space G0/K0 is of hermitian type, i.e. where has coefficient 1 in the maximal root μ, so we assume that the group G0 is not of hermitian type, in other words that has coefficient 2 in μ. Several authors have studied the case where G0/K0 is a quaternionic symmetric space and the inducing holomorphic vector bundle is a line bundle. That is the case where μ is orthogonal to the compact simple roots and the inducing representation is 1–dimensional.

M3 - Working paper

BT - Geometry of the Borel - de Siebenthal discrete series

PB - Department of Mathematical Sciences, Aarhus University

CY - Århus

ER -