TAILIEUCHUNG - Modular symmetry classes of tensors

Then we use modular symmetry classes of tensors to study the polynomial representations of GL(V ), where V is a vector space over a field of characterisitic p. At the end we introduce a non-degenerate bilinear form on a modular symmetry class. Some problems are also given. | Turk J Math 23 (1999) , 417 – 433. ¨ ITAK ˙ c TUB MODULAR SYMMETRY CLASSES OF TENSORS M. Shahryari, M. A. Shahabi Abstract We introduce the notion of modular symmetry classes of tensors and give a necessary and sufficient condition for a modular symmetry class of tensors associated with the full symmetric group to be non-zero. Then we use modular symmetry classes of tensors to study the polynomial representations of GL(V ) , where V is a vector space over a field of characterisitic p. At the end we introduce a non-degenerate bilinear form on a modular symmetry class. Some problems are also given. 1. Introduction Let V be an n-dimensional complex vector space, and G be a permutation group on m elements. Let χ be any irreducible character of G . For any g G , define the operator Pg : m O V → m O V by Pg (v1 ⊗ . . . ⊗ vm ) = vg−1 ⊗ . . . ⊗ vg−1 (m). Then the symmetry class of tensors associated with G and χ is the image of the following symmetry operator Sχ = χ(1) X χ(g)Pg .

• Toán học
• Modular symmetry classes of tensors
• Polynomial representations
• Characterisitic p
• Non degenerate bilinear
• Symmetric group
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