Parthasarathy-Ranga Rao-Varadarajan conjecture

introduction

• PRV conjecture
• notations
  • $\nu$ integral weight
  • $\overline{\nu}$ the dominant integral weight of $W\cdot \nu$
  • $V(\overline{\nu})$ highest weight representation
• $\lambda,\mu$ dominant integral weights and $w\in W$, the module $V(\overline{\lambda+w\mu})$ occurs with multiplicity at least one in $V(\lambda)\otimes V(\mu)$

articles

• Kumar, Shrawan. 1988. “Proof of the Parthasarathy-Ranga Rao-Varadarajan Conjecture.” Inventiones Mathematicae 93 (1): 117–130. doi:10.1007/BF01393689. http://link.springer.com/article/10.1007%2FBF01393689