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- W1556685898 abstract "We construct a large class of examples of the cyclic sieving phenomenon by expoiting the representation theory of semi-simple Lie algebras. Let $M$ be a finite dimensional representation of a semi-simple Lie algebra and let $B$ be the associated Kashiwara crystal. For $rge 0$, the triple $(X,c,P)$ which exhibits the cyclic sieving phenomenon is constructed as follows: the set $X$ is the set of isolated vertices in the crystal $otimes^rB$; the map $ccolon Xrightarrow X$ is a generalisation of promotion acting on standard tableaux of rectangular shape and the polynomial $P$ is the fake degree of the Frobenius character of a representation of $mathfrak{S}_r$ related to the natural action of $mathfrak{S}_r$ on the subspace of invariant tensors in $otimes^rM$. Taking $M$ to be the defining representation of $mathrm{SL}(n)$ gives the cyclic sieving phenomenon for rectangular tableaux." @default.
- W1556685898 created "2016-06-24" @default.
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- W1556685898 date "2009-12-08" @default.
- W1556685898 modified "2023-09-27" @default.
- W1556685898 title "Invariant tensors and the cyclic sieving phenomenon" @default.
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