Linking first occurrence polynomials over F_p by Steenrod operations
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.
Keywords
Cite
@article{arxiv.math/0207213,
title = {Linking first occurrence polynomials over F_p by Steenrod operations},
author = {Pham Anh Minh and Grant Walker},
journal= {arXiv preprint arXiv:math/0207213},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-27.abs.html