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 $V(\lambda)\otimes V(\mu)$

memo

• http://mathoverflow.net/questions/163217/tensor-products-of-two-irreducible-representations-of-reductive-groups-and-their/163239#163239

related items

• Tensor product decompositions of representations of Lie algebras

expositions

• Khare, Apoorva. 2012. “Representations of Complex Semi-simple Lie Groups and Lie Algebras.” arXiv:1208.0416 (August 2). http://arxiv.org/abs/1208.0416.
• Kumar, Shrawan. 2010. “Tensor Product Decomposition.” In Proceedings of the International Congress of Mathematicians. Volume III, 1226–1261. New Delhi: Hindustan Book Agency. http://www.ams.org/mathscinet-getitem?mr=2827839. http://www.unc.edu/math/Faculty/kumar/papers/kumar60.pdf

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