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A probabilistic approach to the Shintani-Casselman-Shalika formula Chhaibi, Reda
Description
Recall that Jacquet's Whittaker function for a group \(G\), in the non-Archimedean case, is essentially proportional to a character of an irreducible representation of the Langlands dual group - a Schur function in the case of \(\text{GL}_n\). This statement is known as the Shintani-Casselman-Shalika formula.
In my opinion, Shintani's proof for \(\text{GL}_n\) is remarkably different from the more general proof by Casselman-Shalika. In this talk, I will present a probabilistic proof that is the natural generalisation of Shintani's. It explains the appearance of the Weyl character formula from a reflection principle for random walks.
Item Metadata
| Title |
A probabilistic approach to the Shintani-Casselman-Shalika formula
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-07-25T08:59
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| Description |
Recall that Jacquet's Whittaker function for a group \(G\), in the non-Archimedean case, is essentially proportional to a character of an irreducible representation of the Langlands dual group - a Schur function in the case of \(\text{GL}_n\). This statement is known as the Shintani-Casselman-Shalika formula.
In my opinion, Shintani's proof for \(\text{GL}_n\) is remarkably different from the more general proof by Casselman-Shalika. In this talk, I will present a probabilistic proof that is the natural generalisation of Shintani's. It explains the appearance of the Weyl character formula from a reflection principle for random walks.
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| Extent |
46 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Institut de Mathématiques de Toulouse
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| Series | |
| Date Available |
2017-02-05
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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 |
10.14288/1.0340867
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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