A survey of modular representation theory II: p-modular systems and blocksShawn Baland, Aberdeen |
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October 22, 2009 AbstractThe main idea behind group representation theory is to use well-understood results from linear algebra to study the structure of finite groups. Similarly, modular representation theory seeks to use well-understood results from ordinary representation theory to study representations where the field characteristic divides the group order. In this lecture, we will examine p-modular systems which, in a manner of speaking, allow us to move back and forth between ordinary representations and modular representations. We will discuss decomposition matrices, Cartan matrices and block idempotents, and then use these structures to calculate the modular representations of the dihedral group of order 12. Time permitting, we will also take a look at block theory and defect groups. |