We show that the fixed-point subvariety of a Nakajima quiver variety under a diagram automorphism is a disconnected union of quiver varieties for the ‘split-quotient quiver’ introduced by Reiten and Riedtmann. As a special case, quiver varieties of type D arise as the connected components of fixed-point subvarieties of diagram involutions of quiver varieties of type A. In the case where the qui...

This paper establishes an equivalence between existence of free involutions on HCP 3 and existence of involutions on S with fixed point set an imbedded S, then a family of counterexamples of the Smith conjecture for imbeddings of S in S are given by known result on HCP . In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smo...

This paper establishes an equivalence between existence of free involutions on HCP 3 and existence of involutions on S with fixed point set an imbedded S, then a family of counterexamples of the Smith conjecture for imbeddings of S in S are given by known result on HCP . In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smo...

We determined the inner products of two conformal vectors with central charge 1 2 whose τ -involutions generates S3 if none of τ -involutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge 1 2 + 20 21 or 4 5 + 6 7 and has a Griess algebra of dimension three or four, respectively.