Noncompact groups of Hermitian symmetric type and factorization (Q2410904)

The authors in this well-written paper investigate Birkhoff (or triangular) factorization that is one of the forms of Bruhat decomposition and root subgroup factorization that they define for elements of a noncompact simple Lie group \(G_0\) of Hermitian symmetric type. For compact groups root subgroup factorization is related to Bott-Samelson desingularization, and many striking applications have been discovered by \textit{J.-H. Lu} [Transform. Groups 4, No. 4, 355--374 (1999; Zbl 0938.22012)]. Characterizations of the Birkhoff components of \(G_0\) for the noncompact Hermitian symmetric case and an analogous construction of root subgroup coordinates for the Birkhoff components are obtained. As in the compact case, the authors show that the restriction of Haar measure to the top Birkhoff component is a product measure in root subgroup coordinates, an interesting result.