Dirichlet for diferent vectors

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Hi. I am trying to fit a GARCH for multiple vectors using a Dirichlet for alpha and beta but It seems like the code can not het the parameters for different vectors.

This is my code

data {
  int<lower=0> T;
  matrix[T, 4] R;
  row_vector<lower=0>[4] sigma1;
	int<lower=0> K;
	int<lower=0> V;
	row_vector<lower=0>[4] omega_star;
	matrix<lower=0>[4, V] alpha_beta_star;
}


parameters {
  row_vector<lower=0,upper=1>[4]  omega;
	row_vector<lower=0,upper=1>[4]  alpha;
	row_vector<lower=0,upper=1>[4] beta;
	simplex[K] alpha_beta[4];
}

transformed parameters{
	matrix<lower=0>[T,4]h;
	for (i in 1:4){
	  h[1,i] = sigma1[i];
	}
	
	for (t in 2:T){
	  for (i in 1:4){
	    	h[t,i] = sqrt(omega[i]
		+ alpha[i] * pow(R[t-1,i], 2)
		+ beta[i] * pow(h[t-1,i],2));
	  }

	}
}

model {
//priors

for (i in 1:4){
  	omega[i] ~ gamma(omega_star[i],2);
  	alpha_beta[i] ~ dirichlet(alpha_beta_star[i]);
}

//likelihood
for (i in 1:4){
  
     R[i] ~ normal(0, h[i])
}


}

Can some one give an advice about how to write the dirichlet?

Thanks

Andrés