GLMM posterior

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data {
int <lower=1> N; //number of data points
vector [N] Reaction; //response variable
//int < lower=1, upper=10> Days[N]; // covariate
int<lower=1> J;// number of subjects
int<lower=1> K; // no of Days
int<lower=1, upper=J> subj[N]; // number of subjects
int<lower=1, upper=K> Days[N]; // number repeated measures (times)

vector[2] beta; // number of fixed effects (intercept and slope)
real <lower=0> sigma_e; //error sd
vector<lower=0> [2] sigma_u; //subject sd
cholesky_factor_corr[2] L_u;
matrix[2,J] z_u;


transformed parameters{
matrix[2,J] u;

u<-diag_pre_multiply(sigma_u, L_u)* z_u;//subject random effects

model {

real mu;
beta [2]~normal(0,100);
L_u~ lkj_corr_cholesky(2.0); //subject random effects

// likelihood
for (i in 1:N){
mu= beta[1]+u[1,subj[i]]+ beta[2]*Days[i]+u[2,subj[i]] * Days[i];
Reaction[i] ~normal(mu,sigma_e);

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where U is refers random intercept and random slope. With the LKJ prior could anybody help me to construct the mathematical form of the posterior. The parameter involves here beta, sigma_e, U and the variance covariance matrix of U,