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Semi-Modules and Crystal Bases via Affine Deligne-Lusztig Varieties

Ryosuke Shimada
Dec 2022
摘要
There are two combinatorial ways of parameterizing the $J_b$-orbits of theirreducible components of affine Deligne-Lusztig varieties for $GL_n$ andsuperbasic $b$. One way is to use the extended semi-modules introduced byViehmann. The other way is to use the crystal bases introduced by Kashiwara andLusztig. In this paper, we give an explicit correspondence between them usingthe crystal structure.
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