Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Semisimple Representations of the Framed g-loop Quiver

  • Choy, Jaeyoo (Department of Mathematics, Kyungpook National University)
  • Received : 2017.04.30
  • Accepted : 2017.07.14
  • Published : 2017.12.23
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Abstract

Let Q be the frame g-loop quiver, i.e. a generalized ADHM quiver obtained by replacing the two loops into g loops. The vector space M of representations of Q admits an involution ${\ast}$ if orthogonal and symplectic structures on the representation spaces are endowed. We prove equivalence between semisimplicity of representations of the ${\ast}-invariant$ subspace N of M and the orbit-closedness with respect to the natural adjoint action on N. We also explain this equivalence in terms of King's stability [8] and orthogonal decomposition of representations.

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References

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