On Automorphism group of a $G$-induced variety

Arpita Nayek; A. J. Parameswaran; Pinakinath Saha

On Automorphism group of a $G$-induced variety

Algebraic Geometry 2024-10-08 v2 Representation Theory

Authors: Arpita Nayek , A. J. Parameswaran , Pinakinath Saha

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 $E.$

Keywords

automorphism group g-induced variety semisimple algebraic group borel subgroup projective b-variety connected component

Cite

@article{arxiv.2302.09960,
  title  = {On Automorphism group of a $G$-induced variety},
  author = {Arpita Nayek and A. J. Parameswaran and Pinakinath Saha},
  journal= {arXiv preprint arXiv:2302.09960},
  year   = {2024}
}

Comments

27 pages, the presentation style and final exposition of the paper were extensively revised based on the reviewer's suggestions

On Automorphism group of a $G$-induced variety

Abstract

Keywords

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