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Tag Archives: induced representations
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
Modular Representation Theory (III)
Let’s work out some explicit examples of modular characters. First, we have a summary of the main results. Let be the modular characters of the simple k[G]modules; they form a basis of Let be those of the projective indecomposable k[G]modules; they form a basis … Continue reading
Quick Guide to Character Theory (III): Examples and Further Topics
G10(a). Character Table of S4 Let’s construct the character table for . First, we have the trivial and alternating representations (see examples 1 and 2 in G1), both of which are clearly irreducible. Next, the action of G on {1, 2, 3, … Continue reading