Answer by Gutiérrez for Bender-Knuth involutions for symplectic (King) tableaux
Let the hyperoctahedral group $\mathbb{S}_n\wr\mathbb{S}_2$ act naturally on the set $\{1, 2, ..., n\} \cup \{1', 2', ..., n'\}$. Then, we can say $\mathbb{S}_n\wr\mathbb{S}_2$ is generated by the...
View ArticleAnswer by Joel Kamnitzer for Bender-Knuth involutions for symplectic (King)...
For any semisimple Lie algebra $ \mathfrak g $ and any crystal $ B $ of a $\mathfrak g$-representation, we have an action of the cactus group $ C_{\mathfrak g} $ on $ B $. We have a surjective group...
View ArticleBender-Knuth involutions for symplectic (King) tableaux
First let me recall the combinatorial theory of the characters of $\mathfrak{gl}_m$, a.k.a., Schur polynomials. For a partition $\lambda$, a semistandard Young tableaux of shape $\lambda$ is a filling...
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