Name
Title | ||
|---|---|---|
Young Tableaux And Linear Independence Of Standard Monomials In Multiminors Of A Multimatrix |
Abstract | ||
|---|---|---|
As a culmination of the efforts of the invariant theorists from Clebsch, Gordan, Young, to Rota. in 1972 Doublet-Rota-Stein proved the Straightening Law which says that the standard monomials in the minors of a matrix X, which correspond to standard bitableaux, form a vector space basis of the polynomial ring K[X] in the indeterminate entries X over the coefficient field K. Now we may ask what happens to this when we consider 'higher dimensional' matrices by using cubical, 4-way, . . . , q-way determinants which were already introduced by Cayley in 1843. In the present paper we show that, for every q > 2, the standard monomials in the multiminors of the multimatrix X are linearly independent over K. In a forthcoming paper it will be shown that they do not span the polynomial ring K[X]. The proof of linear independence given in this paper also applies to the classical case of q = 2. |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1016/0012-365X(91)90467-G | DISCRETE MATHEMATICS |
Keywords | Field | DocType |
linear independence,young tableaux | Discrete mathematics,Combinatorics,Linear independence,Polynomial,Polynomial ring,Matrix (mathematics),Monomial basis,Monomial,Basis (linear algebra),Young tableau,Mathematics | Journal |
Volume | Issue | ISSN |
96 | 1 | 0012-365X |
Citations | PageRank | References |
1 | 0.50 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shreeram S. Abhyankar | 1 | 23 | 6.93 |
| Sudhir R. Ghorpade | 2 | 80 | 12.16 |