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Tag Archives: symmetric group
Polynomials and Representations XXII
Product of Representations Recall that the Frobenius map gives an isomorphism of abelian groups: Let us compute what the product corresponds to on the RHS. For that, we take and where and Multiplication gives where is the partition obtained by sorting Next, we … Continue reading
Polynomials and Representations XXI
We have established that all irreps of are defined over and hence any field of characteristic 0. For convenience we will fix . Twists For any group G and representation over if is a group homomorphism, we can twist as follows: Sometimes, we also … Continue reading
Polynomials and Representations XX
From now onwards, we will assume the base field K has characteristic 0. Example: d=3 Following the previous article, we examine the case of . We get 3 partitions: , and Let us compute for all From the previous article, we have: Since , is … Continue reading
Polynomials and Representations XIX
Representations of the Symmetric Group Let [d] be the set {1,…,d}, and Sd be the group of bijections From here on, we shall look at the representations of Note that this requires a good understanding of representation theory (character theory) of finite groups. To start, let … Continue reading
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Tagged character theory, group actions, representation theory, symmetric group
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