Crystals, semistandard tableaux and cyclic sieving phenomenon

초록

In this paper, we study a new cyclic sieving phenomenon on the set SSTn(lambda) of semistandard Young tableaux with the cyclic action c arising from its U-q(sl(n)-crystal structure. We prove that if A is a Young diagram with (A) < n and gcd(n, vertical bar lambda vertical bar = 1, then the triple (SSTn(lambda), C, q(-k) s lambda (1, q,..., q(n-1))) exhibits the cyclic sieving phenomenon, where C is the cyclic group generated by c. We further investigate a connection between c and the promotion pr and show the bicyclic sieving phenomenon given by c and prTh for hook shape.

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