Gröbner bases of ideals of minors of a symmetric matrix (Q1330061)

Let \(X : = (X_{ij})_{i,j}\) be a symmetric \(n \times n\)-matrix of indeterminates, \(R\) the polynomial ring in \(X_{ij}\), \(1 \leq i \leq j \leq n\), over a field \(K\), and let \(I_ t\) be the ideal of \(R\) generated by all \(t\)-minors of \(X\). The author computes a Gröbner basis for \(I_ t\) and the multiplicity of the quotient ring \(R/I_ t\). For this he first establishes a bijective map between the set of standard tableaux of double shape and the set of monomials in \(R\).