Fri, February 16, 2018
Public Access Category: All |
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- Time:
- 10:30am-11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- 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.
- Time:
- 4:00pm-5:00pm
- Location:
- Room No. 105, Department of Mathematics
- Description:
- Speaker: Dr. Rajeev Gupta , IIT Kanpur
Date: Friday, February 16, 2018
Time: 4:00 pm - 5:00 pm
Venue: Room 105
Title: On a question N. Th. Varopoulos
The abstract of the talk is attached.
- Time:
- 4:00pm-5:00pm
- Location:
- Conference Room, Department of Mathematics
- Description:
- Title : On the distance between two weighted sums of random variables.
Speaker : Professor Vydas Cekanavicius
Vilnius University
Lithuania.
Date: Friday, February 16, 2018
Time: 4.00 pm - 05.00 pm
Venue: Conference Room, Department of Mathematics
Abstract: We discuss the approximation problems between two weighted sums
of the form $w_1X_1+ \ldots +wn_Xn$, where the weights are fixed and the
$Xi$'s are independent or weakly dependent random variables. The Kolmogorov
metric is used to obtain the estimates which, in general, are of the order
$O(n^{-1/2}$.