  The diamond cone is a combinatorial description for a basis of an
indecomposable module for the nilpotent factor $\mathfrak n$ of a semi simple
Lie algebra. After N. J. Wildberger who introduced this notion, this
description was achevied for $\mathfrak{sl}(n)$, the rank 2 semi-simple Lie
algebras and $\mathfrak{sp}(2n)$. In the present work, we generalize these
constructions to the Lie algebras $\mathfrak{so}(2n+1)$. The orthogonal
semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they
form a basis for the shape algebra of $\mathfrak{so}(2n+1)$. Defining the
notion of orthogonal quasistandard Young tableaux, we prove these tableaux give
a basis for the diamond module for $\mathfrak{so}(2n+1)$.

Quantum Algebra