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Decomposition of Induced and Restricted Modules

Induced and Restricted Representation ManipulationThe Noether-Deuring Theoremprove on induced and restricted representationHow to Decompose Representations into Irreducible Ones?Induced Representations from Tensor Product of ModulesDecomposition of An Induced Representation of $GL(2, q)$Representations of a direct productArtin-Wedderburn decomposition of $mathbbF_2[S_5]/J$Decomposing bimodule into irreduciblesQuotient of induced modules

-1

$begingroup$

I am taking a course in representation theory, and as I missed many classes I am having a lot of trouble in dealing with the decomposition of induced and restricted representations. I have no idea how to proceed with questions like this. Can I have some hints or the results to use for solving these problems.

1. Obtain the decomposition of $ big(S^(2,1)otimes S^(3,1)big)uparrow_S_3times S_4^S_7$ into irreducible $S_7$ modules.




2. Obtain the decomposition of $S^(4,1)downarrow_S_3 times S_2^S_5$ as a direct sum of irreducible $S_3 times S_2$ modules.

representation-theory

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jv0174jv0174

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  Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
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  – dantopa
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-1

$begingroup$

I am taking a course in representation theory, and as I missed many classes I am having a lot of trouble in dealing with the decomposition of induced and restricted representations. I have no idea how to proceed with questions like this. Can I have some hints or the results to use for solving these problems.

1. Obtain the decomposition of $ big(S^(2,1)otimes S^(3,1)big)uparrow_S_3times S_4^S_7$ into irreducible $S_7$ modules.




2. Obtain the decomposition of $S^(4,1)downarrow_S_3 times S_2^S_5$ as a direct sum of irreducible $S_3 times S_2$ modules.

representation-theory

share|cite|improve this question

asked Mar 12 at 21:08

jv0174jv0174

1

New contributor

jv0174 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
  $endgroup$
  – dantopa
  Mar 12 at 21:19
  

  
  
  
  

add a comment | 

$begingroup$

I am taking a course in representation theory, and as I missed many classes I am having a lot of trouble in dealing with the decomposition of induced and restricted representations. I have no idea how to proceed with questions like this. Can I have some hints or the results to use for solving these problems.

1. Obtain the decomposition of $ big(S^(2,1)otimes S^(3,1)big)uparrow_S_3times S_4^S_7$ into irreducible $S_7$ modules.




2. Obtain the decomposition of $S^(4,1)downarrow_S_3 times S_2^S_5$ as a direct sum of irreducible $S_3 times S_2$ modules.

representation-theory

share|cite|improve this question

asked Mar 12 at 21:08

jv0174jv0174

1

New contributor

jv0174 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

asked Mar 12 at 21:08

jv0174jv0174

1

New contributor

jv0174 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

asked Mar 12 at 21:08

jv0174jv0174

1

New contributor

jv0174 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 12 at 21:08

jv0174jv0174

1

New contributor

jv0174 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 12 at 21:08

jv0174jv0174

1