Representations Generated by Decomposable TensorsAlgebra & Discrete Mathematics
|Andrew Berget, UC Davis
|Fri, Oct 2 2009, 4:10PM
The cyclic general linear group or symmetric group representation generated by a decomposable tensor contains subtle information about a related matroid. We show how matroids allow us to determine which irreducible representations occur in these cyclic modules as well as how to determine the multiplicities of hook shapes. This will lead us to a new interpretation of the full two-variable Tutte polynomial for realizable matroids. There are many interesting open problems related to such representations and these will be indicated along the way. No familiarity with matroids is assumed.