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Linking first occurrence polynomials over F_p by Steenrod operations | | Pham Anh Minh
; Grant Walker
; | | Date: |
23 Jul 2002 | | Journal: | Algebr. Geom. Topol. 2 (2002) 563-590 | | Subject: | Algebraic Topology MSC-class: 55S10, 20C20 | math.AT | | Abstract: | This paper provides analogues of the results of [G.Walker and R.M.W. Wood, Linking first occurrence polynomials over F_2 by Steenrod operations, J. Algebra 246 (2001), 739--760] for odd primes p. It is proved that for certain irreducible representations L(lambda) of the full matrix semigroup M_n(F_p), the first occurrence of L(lambda) as a composition factor in the polynomial algebra P=F_p[x_1,...,x_n] is linked by a Steenrod operation to the first occurrence of L(lambda) as a submodule in P. This operation is given explicitly as the image of an admissible monomial in the Steenrod algebra A_p under the canonical anti-automorphism chi . The first occurrences of both kinds are also linked to higher degree occurrences of L(lambda) by elements of the Milnor basis of A_p. | | Source: | arXiv, math.AT/0207213 | | Services: | Forum | Review | PDF | Favorites | |
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