Let G be a connected semisimple algebraic group of adjoint type over the field C of complex numbers and B be a Borel subgroup of G. Let F be an irreducible projective B-variety. Then consider the variety E:=G x^B F, which has a natural action of G; we call it the G-induced variety or (G,B)-induced variety. In this article, we compute the connected component containing the identity automorphism of the group of all algebraic automorphisms of some particular G-induced varieties E.

We are grateful to the referee for his/her careful reading and numerous valuable remarks and comments. We are also thankful to Professor Michel Brion for his encouragement and useful comments through e-mail exchanges on a preliminary version of this paper. The first named author would like to thank Chennai Mathematical Institute for the postdoctoral fellowship and the hospitality during her stay. The second and third named authors would like to thank Department of Atomic Energy, Government of India [project no. 12-R&D-TFR-5.01-0500] for the funding. Third named author acknowledges Tata Institute of Fundamental Research for the postdoctoral position and the hospitality during his stay.