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Certain finiteness results for local Kac-Moody groups Ali, Abid
Description
About half a century ago, Simon Gindikin and Fredrick Karpelevich evaluated the well known Harish Chandraâ à ôs \textbf{c}-function for semisimple Lie groups. This solution became known as the Gindikin-Karpelvich formula. While studying the constant term of Eisenstein series on adelic groups, Langland in \emph{Euler Products}, formulated the $p$-adic analogue of \textbf{c}-function and solved this integral. Macdonald independently obtained this formula for $p$-adic Chevalley groups in his lectures notes \emph{Spherical Functions on a Group of p-adic Type}. In Kac-Moody settings, which are infinite dimensional in general, the first challenge is to show that the algebraic analogue of the \textbf{c}-function is well defined. This can be done by proving certain finiteness results. For affine Kac-Moody groups, Braverman, Garland, Kazhdan, and Patnaik (BGKP) did this in 2014. Recently, Auguste H´ebert generalized these results by using the combinatorial objects called \emph{hovels} associated with Kac-Moody groups. We are trying to obtain these finiteness results using the algebraic methods motivated by the work of BGKP. In my talk, I will describe these results and share our progress on it. This is a joint project with Manish Patnaik.
Item Metadata
Title |
Certain finiteness results for local Kac-Moody groups
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-05-12T14:30
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Description |
About half a century ago, Simon Gindikin and Fredrick Karpelevich evaluated the well known Harish Chandraâ à ôs \textbf{c}-function for semisimple Lie groups. This solution became known as the Gindikin-Karpelvich formula. While studying the constant term of Eisenstein series on adelic groups, Langland in \emph{Euler Products}, formulated the $p$-adic analogue of \textbf{c}-function and solved this integral. Macdonald independently obtained this formula for $p$-adic Chevalley groups in his lectures notes \emph{Spherical Functions on a Group of p-adic Type}.
In Kac-Moody settings, which are infinite dimensional in general, the first challenge is to show that the algebraic analogue of the \textbf{c}-function is well defined. This can be done by proving certain finiteness results. For affine Kac-Moody groups, Braverman, Garland, Kazhdan, and Patnaik (BGKP) did this in 2014. Recently, Auguste H´ebert generalized these results by using the combinatorial objects called \emph{hovels} associated with Kac-Moody groups.
We are trying to obtain these finiteness results using the algebraic methods motivated by the work of BGKP. In my talk, I will describe these results and share our progress on it. This is a joint project with Manish Patnaik.
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Extent |
21.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Alberta
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Series | |
Date Available |
2020-12-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0395153
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International