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Linear Representations and Isospectrality with Boundary Conditions

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, Hebrew University, Jerusalem, 91904, Israel

    Ori Parzanchevski

  2. Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Ram Band

Authors
  1. Ori Parzanchevski
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  2. Ram Band
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Correspondence to Ori Parzanchevski.

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Communicated by Carolyn Gordon.

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Parzanchevski, O., Band, R. Linear Representations and Isospectrality with Boundary Conditions. J Geom Anal 20, 439–471 (2010). https://doi.org/10.1007/s12220-009-9115-6

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  • DOI: https://doi.org/10.1007/s12220-009-9115-6

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