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Search: id:A129520
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| A129520 |
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Limited sequence of symmetric groups associate with the exceptional group sequence: as G2,F4,E6,E7,E7.5,E8,E9 ( or better? E11) as A3,S3,A4,S5,"? ",A5,S5. |
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1
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OFFSET
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1,1
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COMMENT
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The calculation by hand based on dimensions of: Dim_Ex(i)-n(i)*Dim_Symm(i)=small_integer The groups E7.5 and E9 are better thought of as E7.6 and E11 when integer results are wanted. The "?" question mark group is a symmetrical group between s4 and A5 with dimension 40; it isn't in any of the books I have or on the web as far as I can find by searching. I'm not an Hecke algebra expert either.
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REFERENCES
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Gareth Jones and David Singerman, Bull. London Math Soc. 28, (1996) pages 561-590 ( A4,S4,A5 on p585)
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EXAMPLE
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14-4*3=2
52-8*6=4
78-5*12=6
133-5*24=13
190-4.6*40=6
248-4*60=8
484-4*120=4
Example:
DimEx(E7.6)/Dim_cartan=190/7.6=25
DimEx(E11)/Dim_cartan=484/11=44
which fit in the sequence of the traditional exceptional groups A118889
as:3, 7, 13, 13, 19, 25, 31,44
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CROSSREFS
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Cf. A118889.
Sequence in context: A101738 A083525 A106213 this_sequence A047167 A054718 A109155
Adjacent sequences: A129517 A129518 A129519 this_sequence A129521 A129522 A129523
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 28 2007
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