Geometric structure of affine Deligne-Lusztig varieties for GL3

Shimada, Ryosuke

doi:10.1016/j.jalgebra.2023.02.015

Journal of Algebra

2023

DOI: 10.1016/j.jalgebra.2023.02.015

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Geometric structure of affine Deligne-Lusztig varieties for GL3

Ryosuke Shimada

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On some simple geometric structure of affine Deligne–Lusztig varieties for $${{\,\textrm{GL}\,}}_n$$

Shimada

2023

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In this paper we study the geometric structure of affine Deligne–Lusztig varieties $$X_{\lambda }(b)$$ X λ ( b ) for $$\textrm{GL}_n$$ GL n and b basic. Motivated by Görtz and He (Camb J Math 3:323–353, 2015) and Chan and Ivanov (Math Ann 380:1801–1890, 2021), we consider a new condition on $$\lambda $$ λ . If this is satisfied, then $$X_{\lambda }(b)$$ X λ ( b ) is the disjoint union of classical Deligne–Lusztig varieties times finite-dimensional affine spaces.

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On some simple geometric structure of affine Deligne–Lusztig varieties for $${{\,\textrm{GL}\,}}_n$$

Shimada

2023

manuscripta math.

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Geometric structure of affine Deligne-Lusztig varieties for GL3

Cited by 1 publication

References 22 publications

On some simple geometric structure of affine Deligne–Lusztig varieties for $${{\,\textrm{GL}\,}}_n$$

On some simple geometric structure of affine Deligne–Lusztig varieties for $${{\,\textrm{GL}\,}}_n$$

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