# 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