I am reading Dummit and Foote Ch 18, trying to understand the basics of Representation Theory.(adsbygoogle = window.adsbygoogle || []).push({});

I need help with clarifying Example 3 on page 844 in the particular case of [itex] S_3 [/itex].

(see the attahment and see page 844 - example 3)

Giving the case for [itex]S_3 [/itex] in the example we have the following situation:

Let [itex]G = S_3 [/itex] and let V be an 3-dimensional vector space over F with basis [itex] e_1 , e_2, e_3 [/itex].

Let [itex] S_3 [/itex] act on V by defining for each [itex] \sigma \in S_3 [/itex] [tex] \sigma \circ e_i = e_{ \sigma (i)} , \ \ \ 1 \leq i \leq n [/tex]

i.e [itex] \sigma [/itex] acts by permuting the subscripts of the basis elements

My problem:

I followed Example 3 page 844 - JUST!!!

I am now trying without success to derive (or write it down anyway) the representation [itex] \phi : G \rightarrow GL(V) [/itex] for the above, and then write down the matrices [itex] \phi (g) [/itex] for every element [itex] \sigma \in S_3 [/itex]

I would be very appreciative of some help.

Peter

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# Representations of Groups - S3

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