|
| | | | |
| | | |
| Stat |
Members: 3657
Articles: 2'599'751
Articles rated: 2609
14 October 2024 |
|
| | | | |
|
Article overview
| |
|
|
The coarse quotient for affine Weyl groups and pseudo-reflection groups | | Tom Gannon
; | | Date: |
1 Jun 2022 | | Abstract: | We study the coarse quotient $mathfrak{t}^*//W^{ ext{aff}}$ of the affine
Weyl group $W^{ ext{aff}}$ acting on a dual Cartan $mathfrak{t}^*$ for some
semisimple Lie algebra. Specifically, we classify sheaves on this space via a
"pointwise" criterion for descent, which says that a
$W^{ ext{aff}}$-equivariant sheaf on $mathfrak{t}^*$ descends to the coarse
quotient if and only if the fiber at each field-valued point descends to the
associated GIT quotient. We also prove the analogous pointwise criterion for
descent for an arbitrary finite group acting on a vector space. Using this, we
show that an equivariant sheaf for the action of a finite pseudo-reflection
group descends to the GIT quotient if and only if it descends to the associated
GIT quotient for every pseudo-reflection, generalizing a recent result of
Lonergan. | | Source: | arXiv, 2206.00175 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
REGISTER