Examples of authmorphism groups of ind-varieties of generalized flags

TL;DR

This paper computes the automorphism groups of certain ind-varieties of generalized flags, highlighting differences from classical flag varieties, and provides new insights into their symmetries.

Contribution

It introduces explicit computations of automorphism groups for ind-grassmannians and flag ind-varieties, revealing novel structural differences from classical cases.

Findings

Automorphism groups of finite and cofinite ind-grassmannians are characterized.

Automorphism group of the ind-variety of maximal flags indexed by positive integers is determined.

Distinct behaviors are identified compared to classical flag varieties.

Abstract

We compute the automorphism groups of finite and cofinite ind-grassmannians, as well as of the ind-variety of maximal flags indexed by Z_{>0}. We pay special attention to differences with the case of ordinary flag varieties.