Commutative character sheaves and geometric types for supercuspidal representations
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Bibliographic record
Abstract
We show that some types for supercuspidal representations of tamely ramified <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -adic groups that appear in Jiu-Kang Yu’s work are geometrizable. To do so, we define a function-sheaf dictionary for one-dimensional characters of arbitrary smooth group schemes over finite fields. In previous work we considered the case of commutative smooth group schemes and found that the standard definition of character sheaves produced a dictionary with a nontrivial kernel. In this paper we give a modification of the category of character sheaves that remedies this defect, and is also extensible to non-commutative groups. We then use these commutative character sheaves to geometrize the linear characters that appear in the types introduced by Jiu-Kang Yu, assuming that the character vanishes on a certain derived subgroup. To define geometric types , we combine commutative character sheaves with Gurevich and Hadani’s geometrization of the Weil representation and Lusztig’s character sheaves.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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