There is a modern viewpoint on combinatorics Young tableaux in Danilov, V. I.; Koshevoy, G. A. Massifs and the combinatorics of Young tableaux. (Russian) Uspekhi Mat. Nauk 60 (2005), no. 2(362), 79--142; translation in Russian Math. Surveys 60 (2005), no. 2, 269–334 (the LS-involutions are considered in Appendix A).
This paper is online here
http://www.mathnet.ru/links/b2797cbfa2d63906937371dbe7b7b519/rm1402.pdf
