The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$
| dc.creator | Di Vincenzo, Onofrio Mario | |
| dc.creator | La Scala, Roberto | |
| dc.date | 2002-05-02 | |
| dc.date.accessioned | 2026-07-07T04:48:14Z | |
| dc.date.available | 2026-07-07T04:48:14Z | |
| dc.description | In this paper it is proved that the ideal $I_w$ of the weak polynomial identities of the superalgebra $M_{1,1}(E)$ is generated by the proper polynomials $[x_1,x_2,x_3]$ and $[x_2,x_1][x_3,x_1][x_4,x_1]$. This is proved for any infinite field $F$ of characteristic different from 2. Precisely, if $B$ is the subalgebra of the proper polynomials of $F< X>$, we determine a basis and the dimension of any multihomogeneous component of the quotient algebra $B / B \cap I_w$. We compute also the Hilbert series of this algebra. One of the main tools of the paper is a variant we found of the Knuth-Robinson-Schensted correspondence defined for single semistandard tableaux of double shape. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0205024 | |
| dc.identifier | http://arxiv.org/abs/math/0205024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63966 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16R10; 16S50; 05E15 | |
| dc.title | The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$ | |
| dc.type | text |