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Description: | Speaker: K. N. Raghavan Affiliation: The Institute of Mathematical Sciences Date & Time: Friday, 16th February, 10:30-11:30am Venue: Ramanujan Hall Title: The KPRV theorem via paths Abstract: Let V and V' be irreducible representations of a complex semisimple Lie algebra g with highest weight vectors v and v' of weights m and m' respectively. For w in the Weyl group, let M(m,m',w) denote the cyclic g-submodule of V tensor V' generated by the vector v tensor wv' (where wv' denotes a non-zero vector in V' of weight wm'). It was conjectured by Kostant and proved by Kumar that the irreducible representation V(m,m',w) whose highest weight is the unique dominant Weyl conjugate of m+wm' occurs with multiplicity exactly one in the decomposition of M(m,m',w) into irreducibles. Since M(m,m',w0) equals V tensor V', where w0 denotes the longest element of the Weyl group, it follows from this that V(m,m',w) occurs in the decomposition of V tensor V'. This corollary was conjectured earlier by Parthasarathy, Ranga Rao, and Varadarajan (PRV) and proved by Mathieu independently of Kumar. There's a subsequent proof by Littelmann of the PRV conjecture using his theory of Lakshmibai-Seshadri paths. I will talk about joint work with Mrigendra Kushwaha and Sankaran Viswanath where we consider such a path approach to Kostant's refinement of the PRV. |

Location: | Ramanujan Hall, Department of Mathematics |

Date: | Friday, February 16, 2018 |

Time: | 10:30am-11:30am IST |

Duration: | 1 hour |

Access: | Public |