Remarks on Reflexive Subcategories

In this article, we study reflexive subcategories of the category of finitely generated modules over Cohen-Macaulay local rings R. One of the main results yields a complete classification of the reflexive subcategories for the case when R is a one-dimensional complete local hypersurface of finite Cohen-Macaulay representation type. The other result yields a one-to-one correspondence between the subclasses of a stable category and the reflexive subcategories over a complete local hypersurface. Then, we attempt to extend the result in Takahashi [8, Proposition 4.4] to a reflexive subcategory.