NONCOMPACT GROUPS OF HERMITIAN SYMMETRIC TYPE AND FACTORIZATION

Research output: Contribution to journalArticle

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Abstract

We investigate Birkhoff (or triangular) factorization and (what we propose to call) root subgroup factorization for elements of a noncompact simple Lie group G0 of Hermitian symmetric type. For compact groups root subgroup factorization is related to Bott–Samelson desingularization, and many striking applications have been discovered by Lu ([5]). In this paper, in the noncompact Hermitian symmetric case, we obtain parallel characterizations of the Birkhoff components of G0 and an analogous construction of root subgroup coordinates for the Birkhoff components. As in the compact case, we show that the restriction of Haar measure to the top Birkhoff component is a product measure in root subgroup coordinates.

Original languageEnglish (US)
Pages (from-to)105-124
Number of pages20
JournalTransformation Groups
Volume22
Issue number1
DOIs
StatePublished - Mar 1 2017

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Factorization
Roots
Subgroup
Desingularization
Product Measure
Haar Measure
Compact Group
Simple group
Triangular
Restriction

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

NONCOMPACT GROUPS OF HERMITIAN SYMMETRIC TYPE AND FACTORIZATION. / Caine, A.; Pickrell, Douglas M.

In: Transformation Groups, Vol. 22, No. 1, 01.03.2017, p. 105-124.

Research output: Contribution to journalArticle

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