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On Automorphism group of a $G$-induced variety (2302.09960v2)
Published 20 Feb 2023 in math.AG and math.RT
Abstract: Let $G$ be a connected semisimple algebraic group of adjoint type over the field $\mathbb{C}$ of complex numbers and $B$ be a Borel subgroup of $G.$ Let $F$ be an irreducible projective $B$-variety. Then consider the variety $E:=G\times{B}F,$ which has a natural action of $G$; we call it $G$-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 $E.$