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advanced_tools:group_theory:induced_representation [2017/11/10 11:38]
jakobadmin created
advanced_tools:group_theory:induced_representation [2017/12/04 08:01]
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-====== Induced Representation ====== 
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-<tabbox Why is it interesting?> ​ 
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-<tabbox Layman> ​ 
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-<​blockquote>​So it turns out that important concepts in representation theory are just constructions in homotopy theory carried out in a context of symmetries, constructions which in more basic settings are familiar logical operations. For example, the type theoretic construction governing the formation of induced representations,​ typically first met as very basic way of expanding an action of a subgroup to an action of the full group, is very basic when carried out on sets and predicates.** For instance, 
- ​consider the case of the set of dogs sent by the function "​owner"​ to the set of people, each dog being assigned its (unique) 
- ​owner. The equivalent of forming an induced representation in this setting is to map any predicate of dogs to a predicate of people, say, "​poodle"​ is sent to "owner of some poodle"​.**</​blockquote>​ 
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-<tabbox Student> ​ 
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-<note tip> 
-In this section things should be explained by analogy and with pictures and, if necessary, some formulas. 
-</​note>​ 
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-<tabbox Researcher> ​ 
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-<note tip> 
-The motto in this section is: //the higher the level of abstraction,​ the better//. 
-</​note>​ 
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-  ​ 
-<tabbox Examples> ​ 
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---> Example1# 
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-<-- 
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---> Example2:# 
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-<-- 
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-<tabbox FAQ> ​ 
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-<tabbox History> ​ 
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-</​tabbox>​ 
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advanced_tools/group_theory/induced_representation.txt ยท Last modified: 2017/11/10 11:38 by jakobadmin