Journal of the
Korean Mathematical Society JKMS

Let $\G$ denote the orthosymplectic Lie superalgebra $spo$ $(2m,1)$. For each irreducible $\G$-module, we describe its character in terms of tableaux. Using this result, we decompose $\otimes^k V$, the $k$-fold tensor product of the natural representation $V$ of $\G$, into its irreducible $\G$-submodules, and prove that the Brauer algebra $B_k(1-2m)$ is isomorphic to the centralizer algebra of $spo(2m,1)$ on $\otimes^k V$ for $m\ge k$.

Keywords: orthosymplectic Lie superalgebra, tensor product representation, centralizer algebra

MSC numbers: 17B10, 05E10