Difference between revisions of "Quiz:Degrees of irreducible representations"

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{Which of the following is ''not'' a possibility for the multiset of the [[degrees of irreducible representations]] of a finite group over a splitting field of characteristic zero?
 
{Which of the following is ''not'' a possibility for the multiset of the [[degrees of irreducible representations]] of a finite group over a splitting field of characteristic zero?
 
|type="()"}
 
|type="()"}
- 1,1 || ''Wrong''. This arises as the degrees of irreducible representations for [[cyclic group:Z2]]. See [[linear representation theory of cyclic group:Z2]].
+
- 1,1  
- 1,1,2 || ''Wrong''. This arises as the degrees of irreducible representations for [[symmetric group:S3]], which can alternatively be viewed as the [[general affine group of degree one]] over [[field:F3]]. See [[linear representation theory of symmetric group:S3]].
+
|| ''Wrong''. This arises as the degrees of irreducible representations for [[cyclic group:Z2]]. See [[linear representation theory of cyclic group:Z2]].
- 1,1,1,3 || ''Wrong''. This arises as the degrees of irreducible representations for [[alternating group:A4]], which can alternatively be viewed as the [[general affine group of degree one]] over [[field:F4]]. See [[linear representation theory of alternating group:A4]].
+
- 1,1,2  
- 1,1,1,1,4 || ''Wrong''. This arises as the degrees of irreducible representations of [[GA(1,5)]], the [[general affine group of degree one]] over [[field:F5]].
+
|| ''Wrong''. This arises as the degrees of irreducible representations for [[symmetric group:S3]], which can alternatively be viewed as the [[general affine group of degree one]] over [[field:F3]]. See [[linear representation theory of symmetric group:S3]].
+ None of the above, i.e., they are all possibilities || ''Right''. (1,1) arises for [[cyclic group:Z2]], the others all arise for the [[general affine group of degree one]] <math>GA(1,q)</math> for <math>q = 3,4,5</math> respectively. See [[linear representation theory of general affine group of degree one over a finite field]].
+
- 1,1,1,3  
 +
|| ''Wrong''. This arises as the degrees of irreducible representations for [[alternating group:A4]], which can alternatively be viewed as the [[general affine group of degree one]] over [[field:F4]]. See [[linear representation theory of alternating group:A4]].
 +
- 1,1,1,1,4  
 +
|| ''Wrong''. This arises as the degrees of irreducible representations of [[GA(1,5)]], the [[general affine group of degree one]] over [[field:F5]].
 +
+ None of the above, i.e., they are all possibilities  
 +
|| ''Right''. (1,1) arises for [[cyclic group:Z2]], the others all arise for the [[general affine group of degree one]] <math>GA(1,q)</math> for <math>q = 3,4,5</math> respectively. See [[linear representation theory of general affine group of degree one over a finite field]].
 
</quiz>
 
</quiz>

Revision as of 16:39, 3 August 2011

1 Which of the following is not a possibility for the multiset of the degrees of irreducible representations of a finite group over a splitting field of characteristic zero?

1,1
1,1,2
1,1,1,3
1,1,1,1,4
None of the above, i.e., they are all possibilities