December 4, 2025manuscripta mathematicaOpen Access

On the semi-infinite Deligne–Lusztig varieties for GSp

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An isomorphism exists between Lusztig’s semi-infinite Deligne–Lusztig variety and an affine variety at infinite level.
A component of an affine Deligne–Lusztig variety can be expressed as a product with a classical variety.
Semi-infinite Deligne–Lusztig varieties allow a realization of X_h at infinite level through components of affine varieties.
Implications for representations reinterpret previous constructions in Lusztig's conjectural framework.

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This analysis highlights the isomorphism in semi-infinite Deligne–Lusztig varieties for GSp, suggesting deeper connections in representation theory.

Teppei Takamatsu (2025) studied this question.

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This analysis highlights the isomorphism in semi-infinite Deligne–Lusztig varieties for GSp, suggesting deeper connections in representation theory.