Pieri Rules for Classical Groups and Equinumeration between Generalized Oscillating Tableaux and Semistandard Tableaux
Keywords:
Standard tableuax, Oscillating tableaux, Semistandard tableaux, Pieri rules
Abstract
We present several equinumerous results between generalized oscillating tableaux and semistandard tableaux and give a representation-theoretic proof to them. As one of the key ingredients of the proof, we provide Pieri rules for the symplectic and orthogonal groups.