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On irreducible representations of Fuchsian groups

Part of: Algebraic groups Families, fibrations

Published online by Cambridge University Press:  27 August 2024

Vikraman Balaji Open the ORCID record for Vikraman Balaji [Opens in a new window]  and
Yashonidhi Pandey
Vikraman Balaji*
Affiliation:
Chennai Mathematical Institute, H1 Sipcot IT Park, Siruseri, Kelambakkam 603103, India
Yashonidhi Pandey
Affiliation:
Indian Institute of Science Education and Research Mohali, Mohali Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306, India e-mail: [email protected] [email protected]
*
e-mail: [email protected]
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Abstract

Let ${\mathcal {R}} \subset \mathbb {P}^1_{\mathbb {C}}$ be a finite subset of markings. Let G be an almost simple simply-connected algebraic group over $\mathbb {C}$. Let $K_G$ denote the compact real form of G. Suppose for each lasso l around the marked point, a conjugacy class $C_l$ in $K_G$ is prescribed. The aim of this paper is to give verifiable criteria for the existence of an irreducible homomorphism of $\pi _{1}(\mathbb P^1_{\mathbb {C}} \,{\backslash}\, {\mathcal {R}})$ into $K_G$ such that the image of l lies in $C_l$.

Keywords

Bruhat–Tits group schemeparahoric groupModuli stackGromov–Wittenstability

MSC classification

Primary: 14L15: Group schemes 14D23: Stacks and moduli problems 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 4 , December 2024 , pp. 970 - 990
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

To Apurv Pandey

The support of Science and Engineering Research Board under Mathematical Research Impact Centric Support File number: MTR/2017/000229 is gratefully acknowledged.

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