Combinatorial bases of principal subspaces for affine Lie algebra of type B_2^(1)

We consider principal subspaces $W_{L(k{\mathrm{\Lambda }}_0)}$ and $W_{N(k{\mathrm{\Lambda }}_0)}$ of standard module $L(k{\mathrm{\Lambda }}_0)$ and generalized Verma module $N(k{\mathrm{\Lambda }}_0)$ at level $k\ge 1$ for affine Lie algebra of type $B_2^{(1)}$. By using the theory of vertex operator algebras, we find combinatorial bases of principal ubspaces in terms of quasi-particles. From quasi-particle bases, we obtain character formulas for $W_{L(k{\mathrm{\Lambda }}_0)}$ and $W_{N(k{\mathrm{\Lambda }}_0)}$.