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Exotic fusion systems, spetses and counting conjectures Semeraro, Jason
Description
Let G=G(q) be a finite reductive group with Weyl group W. A long time ago Malle noticed that the process by which one calculates the unipotent character degrees of G from the Iwahori-Hecke algebra of W works just as well if W is replaced by a *complex* reflection group (with certain properties). A "spets" is the mysterious object which replaces G in this situation, named after the Greek island Spetses on which these observations were first made. Now suppose l is prime and (l,q)=1. I will argue via the theory of l-compact groups in algebraic topology that we know the l-fusion system of a spets G(q). Moreover, I claim this observation can be combined with results of Cabanes--Enguehard in Deligneâ Lusztig theory to provide degrees of characters in the principal l-block of G. We thus have all the ingredients necessary to formulate exotic counting conjectures inspired by those of Alperin, Dade, Robinson and others. I will explain the proof of such a conjecture when l=2.
Item Metadata
Title |
Exotic fusion systems, spetses and counting conjectures
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-08-27T14:01
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Description |
Let G=G(q) be a finite reductive group with Weyl group W. A long time ago Malle noticed that the process by which one calculates the unipotent character degrees of G from the Iwahori-Hecke algebra of W works just as well if W is replaced by a *complex* reflection group (with certain properties). A "spets" is the mysterious object which replaces G in this situation, named after the Greek island Spetses on which these observations were first made. Now suppose l is prime and (l,q)=1. I will argue via the theory of l-compact groups in algebraic topology that we know the l-fusion system of a spets G(q). Moreover, I claim this observation can be combined with results of Cabanes--Enguehard in Deligneâ Lusztig theory to provide degrees of characters in the principal l-block of G. We thus have all the ingredients necessary to formulate exotic counting conjectures inspired by those of Alperin, Dade, Robinson and others. I will explain the proof of such a conjecture when l=2.
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Extent |
46.0 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 Leicester
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Series | |
Date Available |
2020-02-24
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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 |
10.14288/1.0388681
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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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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International