We present a method for constructing families of isospectral systems, using linear representations of finite groups. We focus on quantum graphs, for which we give a complete treatment. However, the method presented can be applied to other systems such as manifolds and two-dimensional drums. This is demonstrated by reproducing some known isospectral drums, and new examples are obtained as well. In particular, Sunada’s method (Ann. Math. 121, 169–186, 1985) is a special case of the one presented.
|Translated title of the contribution||Linear Representations and Isospectrality with Boundary Conditions|
|Pages (from-to)||439 - 471|
|Number of pages||33|
|Journal||Journal of Geometric Analysis|
|Volume||20, no 2|
|Publication status||Published - Apr 2010|