Abstract
We count the number of isomorphism classes of hom-orthogonal partial tilting modules over path algebras of Dynkin quiver of type đž n , đ» n , đŒ n . This number is independent on the choice of an orientation of the arrows, and the number for đž n or đ» n -type can be expressed as a special value of a hypergeometric function. As a consequence of our theorem, we obtain a minimum value of the number of basic relative invariants of corresponding regular prehomogeneous vector spaces.
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