Linking first occurrence polynomials over F_p by Steenrod operations

Details Linking first occurrence polynomials over F_p by Steenrod operations Linking first occurrence polynomials over F_p by Steenrod operations

2002-07-23

arxiv.org/abs/math/0207213v1

Algebr. Geom. Topol. 2 (2002) 563-590

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-27.abs.html

Scientific paper

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.

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