Department of Mathematics

Indian Institute of Science

Bangalore 560 012






Mr. Manish  Kumar
Affiliation : IISc, Bangalore

Subject Area






Department of Mathematics, Lecture Hall I




11:00 am.




July 13, 2016 (Wednesday)



"Analytic vectors for representation of Lie groups"


Let U denote a strongly continuous representation of a Lie groupG on a Banach space H and let dU denote the corresponding representation on the Lie algebra g of the group. We define the smooth and analytic vectors for this representation. We also define the analytic vectors for a family of operators (unbounded) on the banach space H. Then we find a relation between the analytic vectors of the representation U and those for the family of operators dU(X_i) for some basis {X_i} of the Lie algebra g. Through this relation, we try to characterize the analytic vectors for representation of some particular groups, specifically, the one parameter unitary groups, the Heisenberg groups, the group of affine transformations and non-compact simple groups.