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Find a matrix M such that M-¹0 (8) M = (19) for every element g € S3. Conclude that the representation is isomorphic to a direct sum of the trivial and alternating representations.

Find a matrix M such that M-¹0 (8) M = (19) for every element g € S3. Conclude that the representation is isomorphic to a direct sum of the trivial and alternating representations.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find a matrix M such that M-¹ (8) M = (9) for every element g € S3. Conclude that the representation is isomorphic to a direct sum of the trivial and alternating representations.
Transcribed Image Text:Find a matrix M such that M-¹ (8) M = (9) for every element g € S3. Conclude that the representation is isomorphic to a direct sum of the trivial and alternating representations.
Consider the following map defined on the symmetric group S3: Þ: S3 → GL₂(R) given by: Þ(e) = Þ((123)) = Þ((132)) = (19) ((12)) = ((13)) =((23))= -29 20 -42 29 (a) Show that map & defines a representation of S3.
Transcribed Image Text:Consider the following map defined on the symmetric group S3: Þ: S3 → GL₂(R) given by: Þ(e) = Þ((123)) = Þ((132)) = (19) ((12)) = ((13)) =((23))= -29 20 -42 29 (a) Show that map & defines a representation of S3.
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