On some Airy sheaves of Laurent type

Nicholas M. Katz; Antonio Rojas-León; Pham Huu Tiep

doi:10.1007/s40879-024-00770-0

On some Airy sheaves of Laurent type

Nicholas M. Katz, Antonio Rojas-León, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study certain one-parameter families of exponential sums of Airy–Laurent type. Their general theory was developed in Katz and Tiep (Airy sheaves of Laurent type: an introduction, https://web.math.princeton.edu/~nmk/kt31_11sept.pdf). In the present paper, we make use of that general theory to compute monodromy groups in some particularly simple families (in the sense of “simple to remember"), realizing Weyl groups of type E₆ and E₈.

Original language	English (US)
Article number	65
Journal	European Journal of Mathematics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s40879-024-00770-0
State	Published - Dec 2024

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

11T23
20C15
20C33
20D06
20G40
Airy sheaves
Local systems
Monodromy groups
Weyl groups

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10.1007/s40879-024-00770-0

Cite this

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abstract = "We study certain one-parameter families of exponential sums of Airy–Laurent type. Their general theory was developed in Katz and Tiep (Airy sheaves of Laurent type: an introduction, https://web.math.princeton.edu/\textasciitilde{}nmk/kt31\_11sept.pdf). In the present paper, we make use of that general theory to compute monodromy groups in some particularly simple families (in the sense of “simple to remember{"}), realizing Weyl groups of type E6 and E8.",

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AU - Katz, Nicholas M.

AU - Rojas-León, Antonio

AU - Tiep, Pham Huu

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/12

Y1 - 2024/12

N2 - We study certain one-parameter families of exponential sums of Airy–Laurent type. Their general theory was developed in Katz and Tiep (Airy sheaves of Laurent type: an introduction, https://web.math.princeton.edu/~nmk/kt31_11sept.pdf). In the present paper, we make use of that general theory to compute monodromy groups in some particularly simple families (in the sense of “simple to remember"), realizing Weyl groups of type E6 and E8.

AB - We study certain one-parameter families of exponential sums of Airy–Laurent type. Their general theory was developed in Katz and Tiep (Airy sheaves of Laurent type: an introduction, https://web.math.princeton.edu/~nmk/kt31_11sept.pdf). In the present paper, we make use of that general theory to compute monodromy groups in some particularly simple families (in the sense of “simple to remember"), realizing Weyl groups of type E6 and E8.

KW - 11T23

KW - 20C15

KW - 20C33

KW - 20D06

KW - 20G40

KW - Airy sheaves

KW - Local systems

KW - Monodromy groups

KW - Weyl groups

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AN - SCOPUS:85208752385

SN - 2199-675X

VL - 10

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 4

M1 - 65

ER -

On some Airy sheaves of Laurent type

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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