Standard polytabloid ($e_t(t\text{ a standard Young tableau})$)

A standard polytabloid is the polytabloid associated with a standard Young tableau. The standard polytabloids of one shape form a basis of the corresponding Specht module. For linear independence, sort each row of a tabloid increasingly and compare row-reading words lexicographically. In the column antisymmetrization of a standard tableau, the identity term is its unique least row word: in the first row affected by a nontrivial column permutation, each moved-in entry is larger than the entry it replaces. Hence its coefficient is one, and all other terms are larger. Distinct standard tableaux have distinct least tabloids, so a linear relation is impossible by taking its least nonzero term. Spanning is the straightening part of the standard polytabloid basis theorem.