Linear Representations and Isospectrality with Boundary Conditions
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- Parzanchevski, O. & Band, R. J Geom Anal (2010) 20: 439. doi:10.1007/s12220-009-9115-6
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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.