Details:
Title  Standard monomials for partitions.  Author(s)  Gleb Gusev, Lajos Rónyai  Type  Article in Journal  Abstract  Let F be a field, and α0,...,αk1 be k distinct elements of F. Let λ =(λ1,...,λk) be a partition of n and V λ be the set of all vectors v=(v 1,...,v n)∈ F n such that {j ∈ [n] : v j=αi}=λi+1 for 0≦ i ≦\ k1. We describe the lexicographic standard monomials of the ideal of polynomials from F[x 1,...,x n] which vanish on the set V λ. In the proof we give a new description of the orthogonal complement (S λ)⊥ (with respect to the James scalar product) of the Specht module S λ. As applications, a basis of (S λ)⊥ is exhibited, and we obtain a combinatorial description of the Hilbert function of V λ.. Our approach gives also the deglex standard monomials of V λ, and hence provides a new proof of a result of A. M. Garsia and C. Procesi [10].  Keywords  Gröbner basis, standard monomial, tableau  ISSN  02365294; 15882632/e 
URL 
http://link.springer.com/article/10.1007%2Fs1047400600491 
Language  English  Journal  Acta Math. Hung.  Volume  111  Number  3  Pages  193212  Publisher  Springer Netherlands, Dordrecht; Akad  Year  2006  Edition  0  Translation 
No  Refereed 
No 
