The genus one complex quantum Chern-Simons representation of the mapping class group

Jørgen Ellegaard Andersen; Simone Marzioni

doi:10.1142/S0218216523400096

The genus one complex quantum Chern-Simons representation of the mapping class group

Jørgen Ellegaard Andersen^*, Simone Marzioni

^*Corresponding author for this work

Aarhus University

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

In this paper, we compute explicitly, following Witten's prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to any simple and simply connected complex gauge group G_ℂ. We use a generalization of the Weil-Gel'fand-Zak transform to exhibit an explicit expression for the representation.

Original language	English
Article number	2340009
Journal	Journal of Knot Theory and Its Ramifications
ISSN	0218-2165
DOIs	https://doi.org/10.1142/S0218216523400096
Publication status	E-pub ahead of print - 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.

Keywords

Complex quantum Chern-Simons theory
Genus one Moduli spaces
Geometric quantization
Hitchin-Witten connection

Documents & Links

10.1142/S0218216523400096

Cite this

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title = "The genus one complex quantum Chern-Simons representation of the mapping class group",

abstract = "In this paper, we compute explicitly, following Witten's prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to any simple and simply connected complex gauge group Gℂ. We use a generalization of the Weil-Gel'fand-Zak transform to exhibit an explicit expression for the representation.",

keywords = "Complex quantum Chern-Simons theory, Genus one Moduli spaces, Geometric quantization, Hitchin-Witten connection",

author = "{Ellegaard Andersen}, J{\o}rgen and Simone Marzioni",

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year = "2023",

doi = "10.1142/S0218216523400096",

language = "English",

journal = "Journal of Knot Theory and Its Ramifications",

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T1 - The genus one complex quantum Chern-Simons representation of the mapping class group

AU - Ellegaard Andersen, Jørgen

AU - Marzioni, Simone

PY - 2023

Y1 - 2023

N2 - In this paper, we compute explicitly, following Witten's prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to any simple and simply connected complex gauge group Gℂ. We use a generalization of the Weil-Gel'fand-Zak transform to exhibit an explicit expression for the representation.

AB - In this paper, we compute explicitly, following Witten's prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to any simple and simply connected complex gauge group Gℂ. We use a generalization of the Weil-Gel'fand-Zak transform to exhibit an explicit expression for the representation.

KW - Complex quantum Chern-Simons theory

KW - Genus one Moduli spaces

KW - Geometric quantization

KW - Hitchin-Witten connection

U2 - 10.1142/S0218216523400096

DO - 10.1142/S0218216523400096

M3 - Journal article

AN - SCOPUS:85176559971

SN - 0218-2165

JO - Journal of Knot Theory and Its Ramifications

JF - Journal of Knot Theory and Its Ramifications

M1 - 2340009

ER -

The genus one complex quantum Chern-Simons representation of the mapping class group

Abstract

Bibliographical note

Keywords

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