Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules

2020/10/22 by Marc Besson, Besson, Marc, Jiuzu Hong +1 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2010.11357

Abstract

Let \mathscrG be a special parahoric group scheme of twisted type over the ring of formal power series over ℂ, excluding the absolutely special case of A_2ℓ⁽²⁾. Using the methods and results of Zhu, we prove a duality theorem for general \mathscrG : there is a duality between the level one twisted affine Demazure modules and the function rings of certain torus fixed point subschemes in affine Schubert varieties for \mathscrG. Along the way, we also establish the duality theorem for E₆. As a consequence, we determine the smooth locus of any affine Schubert variety in the affine Grassmannian of \mathscrG. In particular, this confirms a conjecture of Haines and Richarz.

Citations

• The Partial Order of Dominant Weights

Cited by

• A Local Characterization of Unions of Demazure Crystals
• Normality of Schubert varieties in affine Grassmannians II: The tamely ramified case

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