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On tight projective designs
Authors:Yu. I. Lyubich
Affiliation:(1) Department of Mathematics, Technion, Haifa, 32000, Israel
Abstract:It is shown that among all tight designs in $${mathbb {FP}^n neq mathbb {RP}^1}$$ , where $${mathbb {F}}$$ is $${mathbb {R}}$$ or $${mathbb {C}}$$ , or $${mathbb {H}}$$ (quaternions), only 5-designs in $${mathbb {CP}^1}$$ (Lyubich, Shatalora Geom Dedicata 86: 169–178, 2001) have irrational angle set. This is the only case of equal ranks of the first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
Keywords:Projective design  Angle set  Bose-Mesner algebra
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