Richardson, R. W.; Springer, T. A. Complements to ‘The Bruhat order on symmetric varieties’. (English) Zbl 0826.20045 Geom. Dedicata 49, No. 2, 231-238 (1994). Summary: We give several complements to the paper mentioned in the title [ibid. 35, No. 1-3, 389-436 (1990; Zbl 0704.20039)]. Our main result shows that the partial order on the set \(\mathcal I\) of twisted involutions in the Weyl group \(W\), which was introduced in the earlier paper, agrees with the partial order on \(\mathcal I\) induced by the usual Bruhat order on \(W\). Cited in 3 ReviewsCited in 39 Documents MSC: 20G15 Linear algebraic groups over arbitrary fields 20G05 Representation theory for linear algebraic groups 14L30 Group actions on varieties or schemes (quotients) Keywords:connected reductive linear algebraic groups; automorphisms; symmetric variety; Borel subgroups; double cosets; orbits; actions; Zariski closure; partial orders; twisted involutions; Weyl groups; Bruhat order Citations:Zbl 0704.20039 PDFBibTeX XMLCite \textit{R. W. Richardson} and \textit{T. A. Springer}, Geom. Dedicata 49, No. 2, 231--238 (1994; Zbl 0826.20045) Full Text: DOI References: [1] Borel, A.,Linear Algebraic Groups (2nd edn) Springer-Verlag, New York, Berlin, Heidelberg, 1991. · Zbl 0726.20030 [2] Borel, A. and Tits, J., ’Groupes réductifs’,Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150. · Zbl 0145.17402 · doi:10.1007/BF02684375 [3] Deodhar, V. V., ’Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function’,Invent. Math. 39 (1977), 187–198. · Zbl 0346.20032 · doi:10.1007/BF01390109 [4] Richardson, R. W. and Springer, T. A., ’The Bruhat order on symmetric varieties’,Geom. Dedicata 35 (1990), 389–436. · Zbl 0704.20039 · doi:10.1007/BF00147354 [5] Springer, T. A., ’Some results on algebraic groups with involutions’,Advanced Studies in Pure Math., Vol. 6,Algebraic Groups and Related Topics, Kinokuniya/North Holland, 1985, pp. 525–543. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.