$$\mathbb{K}$$-homogeneous tuple of operators on bounded symmetric domains

Let Ω be an irreducible bounded symmetric domain of rank r in ℂd. $$\mathbb{K}$$ the maximal compact subgroup identity component G biholomorphic automorphism group Ω. The consisting linear transformations acts naturally on any d-tuple T = (T1, …, Td) commuting operators. If orbit this action modulo unitary equivalence is a singleton, then we say that -homogeneous. In paper, obtain model for certain class -homogeneous as operators multiplication by coordinate functions z1, zd reproducing kernel Hilbert space holomorphic defined Using criterion (i) boundedness, (ii) membership Cowen-Douglas class, (iii) and similarity these d-tuples. particular, show adjoint weighted Bergman spaces are B1(Ω). For 2, explicit description operator $$\sum\nolimits_{i 1}^d {T_i^\ast {T_i}} $$ given. general, based formula, make conjecture giving form operator.