Computing the ℤ₂-Cocharacter of 3 × 3 Matrices of Odd Degree

Abstract

Let F be a field of characteristic 0 and A = M _{2, 1}(F) the algebra of 3 × 3 matrices over F endowed with the only non trivial ℤ₂-grading. Aver'yanov in [1] determined a set of generators for the T ₂-ideal of graded identities of A. Here we study the identities in variables of homogeneous degree 1 via the representation theory of the symmetric group, and we determine the decomposition of the corresponding character into irreducibles.

Key Words:

• Cocharacter
• Grading
• Polynomial identity

2010 Mathematics Subject Classification:

• Primary: 16R10
• 16R50
• 16W55

Notes

Communicated by S. Sehgal.