6533b82ffe1ef96bd129489b
RESEARCH PRODUCT
Cocharacters of Bilinear Mappings and Graded Matrices
Stefania AquéAntonio Giambrunosubject
Multilinear mapDegree (graph theory)Group (mathematics)General MathematicsField (mathematics)Polynomial identitySpace (mathematics)CocharacterCombinatoricsGradingRepresentation theory of the symmetric groupSymmetric groupLinear algebraMathematicsdescription
Let Mk(F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow Mk(F) with the elementary grading induced by the k-tuple (1,...,1,g) where g ∈ G, g2 ≠ 1. Then the graded identities of Mk(F) depending only on variables of homogeneous degree g and g − 1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g − 1 and we find an explicit decomposition of the corresponding graded cocharacter into irreducibles.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-09-07 | Algebras and Representation Theory |