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arXiv · 2404.03928

On isomorphisms of ind-varieties of generalized flags

Lucas Fresse·Ivan Penkov
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Abstract

Ind-varieties of generalized flags have been studied for two decades. However, a precise statement of when two such ind-varieties, one or both being possibly ind-varieties of isotropic generalized flags, are isomorphic, has been missing in the literature. Using some recent results on the structure of ind-varieties of generalized flags, we establish a criterion for the existence of an isomorphism as above. Our result claims that, with only two exceptions, isomorphisms of ind-varieties of generalized flags are induced by isomorphisms of respective generalized flags. The exceptional isomorphisms correlate with a well-known result of A. Onishchik from 1963.

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Lucas Fresse, Ivan Penkov. 2024-04-05. On isomorphisms of ind-varieties of generalized flags. https://arxiv.org/abs/2404.03928

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