The well-known RSK correspondence established the connection between table pair (P,Q) and the permutations in symmetry group Sn(Coxeter group of type A). Also, there is a similar correspondence for the hyperoctahedral group Bn (Coxeter group of type B)(see e.g. Stanley Some aspects of groups acting on finite posets. J. Combin. Theory Ser. A 32 (1982) 132–161.). My question is: Is there a similar correspondence for Coxeter group of type D, i.e., How to represent the even signed permutations by Young tableaux?
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3$\begingroup$ Cedric Lecouvey, Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$, arXiv:math/0211444v1 claims a bumping algorithm in type D. (h/t Travis Scrimshaw) $\endgroup$– darij grinbergMay 30, 2018 at 19:50
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2$\begingroup$ @Sam a dozen retags of old questions in two hours, driving newer questions off the front page – please don't do that. Do three or four a day, please. $\endgroup$– Gerry MyersonSep 13, 2020 at 22:47
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$\begingroup$ @GerryMyerson: sorry; got it. $\endgroup$– Sam HopkinsSep 13, 2020 at 22:49
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