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advanced_tools:group_theory:induced_representation [2017/12/04 07:01] (current)
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 +====== Induced Representation ======
 +
 +<tabbox Why is it interesting?> ​
 +
 +<tabbox Layman> ​
 +
 +<​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>​
 +  ​
 +<tabbox Student> ​
 +
 +<note tip>
 +In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
 +</​note>​
 + 
 +<tabbox Researcher> ​
 +
 +<note tip>
 +The motto in this section is: //the higher the level of abstraction,​ the better//.
 +</​note>​
 +
 +  ​
 +<tabbox Examples> ​
 +
 +--> Example1#
 +
 + 
 +<--
 +
 +--> Example2:#
 +
 + 
 +<--
 +
 +<tabbox FAQ> ​
 +  ​
 +<tabbox History> ​
 +
 +</​tabbox>​
 +
  
advanced_tools/group_theory/induced_representation.txt ยท Last modified: 2017/12/04 07:01 (external edit)