Pieri rules for classical groups and equinumeration between generalized   oscillating tableaux and semistandard tableaux
  We present several equinumerous results between generalized oscillating tableaux and semistandard tableaux and give a representation-theoretical proof to them. As one of the key ingredients of the proof, we provide Pieri rules for the symplectic and orthogonal groups. 
Soichi Okada
math.CO math.RT