Robinson-Schensted-Knuth Correspondence and Weak Polynomial Identities of M1,1(E)

• 来源期刊: 代数集刊（英文版）
• 关键词: weak polynomial identities superalgebras double tableaux
• 年，卷（期）: 2005,（2）
• 页码范围: 333-349
• 页数: 17页
• 语种: 英文

摘要

In this paper, it is proved that the ideal Iω of the weak polynomial identities of the superalgebra M1,1(E) is generated by the p roper polynomials [x1,x2, x3] and [x2,x1][xa,x1][x4, x1]. This is proved for any infinite field F of characteristic different a basis and the dimension of any multihomogeneous component of the quotient algebra B/(B ∩ Iw). We also compute the Hilbert series of this algebra. One of the main tools of this paper is a variant we found of the Robinson-Schensted-Knuth correspondence defined for single semistandard tableaux of double shape.