Linking first occurrence polynomials over F2 by Steenrod operations

[摘要] It is proved that for every irreducible representation L(A) of the full matrix semi-group group M-n(F-2), the first occurrence of L(A) as a composition factor in the polynomial algebra P =F-2[x(1),..., x(n)] is linked by a Steenrod operation to the first occurrence of L(A) as a submodule in P. This Steenrod operation is given explicitly as the image of an admissible monomial in the STeenrod squares Sq(r) under the canonical anti-automorphism X of the mod 2 Steenrod algebra A. The first occurrences of both kinds are also linked to higher degree occurrences of L(A) by elements of the Milnor basis of A. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15