I was learning from Elements of statistics p.109 under the topic LINEAR DISCRIMINANT ANALYSIS

and I saw the function below for linear discriminant function

$\delta_k = X^T\sum^{-1}\mu_k -\frac{1}{2}\mu_k^T\mu_k+ \log\pi_k$

where

$\pi_k = N_k/N$ where $N_k$ is the number of class-k observations;

$\mu_k$ = $\sum_{g_i = k} x_i/N_k$

$\sum = \sum_{k=1}^k\sum_{g_i = k}(x_i - \mu_k)(x_i - \mu_k)^T/(N - K)$

Please I want know the parameters for this function (I am thinking is $\mu_k$ ) and how come it has (K-1) x (p + 1) parameters