Can you tell me about any genetic conditions which causes low platelets?

Low platelets: Low platelet counts are usually not representative of any specific genetic condition, but reflect chronic illness, liver disease, or bone marrow dysfunction. There are some autoimmune diseases such as ITP [idiopathic thrombocytopenia] which occur in people with Lupus, Rheumatoid Arthritis, etc, which have a genetic component. I would consult a genetic counselor for more information.

Genetic low platelet: Rare. I see none. X-linked thrombocytopenia, Wiskott-Aldrich syndrome, TTP (familial form), Dyserythropoietic anemia and thrombocytopenia, Thrombocytopenia-absent radium syndrome, Bernard-Soulier syndrome, MYH9-related thrombocytopenia, etc.