= Standard polytabloid basis
The <polytabloids> $e_t$ indexed by <standard Young tableaux> of shape $\lambda$ form a basis of $S^\lambda$ over every <field>, and a basis of its integral lattice over $\mathbb Z$. Column antisymmetry and <Garnir relations> straighten any <polytabloid> into this set. Ordering leading <tabloids> by the rows containing successive entries makes the corresponding coefficient <matrix> triangular with diagonal entries one, proving independence. In particular the <dimension> is the standard-tableau count in every characteristic.
Back to article page
