Details:
| Title | Standard monomials for partitions. | | Author(s) | Gleb Gusev, Lajos | | Type | Article in Journal | | Abstract | Let F be a field, and α0,...,αk-1 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 ≦\ k-1. 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 | | | ISSN | 0236-5294; 1588-2632/e |
| URL |
http://link.springer.com/article/10.1007%2Fs10474-006-0049-1 |
| Language | English | | Journal | Acta Math. Hung. | | Volume | 111 | | Number | 3 | | Pages | 193--212 | | Publisher | Springer Netherlands, Dordrecht; Akad | | Year | 2006 | | Edition | 0 | | Translation |
No | | Refereed |
No |
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