The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$

Details The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$ The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$

2002-05-02

arxiv.org/abs/math/0205024v1

Mathematics

Rings and Algebras

19 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Knuth-Robinson-Schensted correspondence and the Weak Polynomial Identities of $M_{1,1}(E)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-232337