Two Problems on Cartan Domains
نویسنده
چکیده
1. Unitary Geometry on Exceptional Cartan Domains In 1935, E.Cartan classified all symmetric bounded domains. He prived that there exit only six types of irreducible bounded symmetric domains in C. They can be realized as follows: RI(m,n) = {Z ∈ Cmn|I − ZZ ′ > 0, Z − (m,n) matrix} RIIp = {Z ∈ Cp(p+1)/2|I − ZZ ′ > 0, Z − symmetric matric of degree p} RIIIq = {Z ∈ Cq(q−1)/2|I − ZZ ′ > 0, Z − skew symmetric matrix of degree q} RIV (n) = {z = (z1, · · · , zn) ∈ Cn|1 + |zz′|2 − 2zz′ > 0, 1− |zz′|2 > 0} or
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