Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918101897969664 |
|---|---|
| author | Besson, Marc Hong, Jiuzu |
| author_facet | Besson, Marc Hong, Jiuzu |
| contents | Let $\mathscr{G}$ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb{C}$, excluding the absolutely special case of $A_{2\ell}^{(2)}$. Using the methods and results of Zhu, we prove a duality theorem for general $\mathscr{G}$ : 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 $\mathscr{G}$. Along the way, we also establish the duality theorem for $E_6$. As a consequence, we determine the smooth locus of any affine Schubert variety in the affine Grassmannian of $\mathscr{G}$. In particular, this confirms a conjecture of Haines and Richarz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_11357 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules Besson, Marc Hong, Jiuzu Representation Theory Algebraic Geometry 14M15, 81R10 Let $\mathscr{G}$ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb{C}$, excluding the absolutely special case of $A_{2\ell}^{(2)}$. Using the methods and results of Zhu, we prove a duality theorem for general $\mathscr{G}$ : 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 $\mathscr{G}$. Along the way, we also establish the duality theorem for $E_6$. As a consequence, we determine the smooth locus of any affine Schubert variety in the affine Grassmannian of $\mathscr{G}$. In particular, this confirms a conjecture of Haines and Richarz. |
| title | Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules |
| topic | Representation Theory Algebraic Geometry 14M15, 81R10 |
| url | https://arxiv.org/abs/2010.11357 |