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2002 Linking first occurrence polynomials over $\mathbb{F}_p$ by Steenrod operations
Phạm Anh Minh, Grant Walker
Algebr. Geom. Topol. 2(1): 563-590 (2002). DOI: 10.2140/agt.2002.2.563

Abstract

This paper provides analogues of the results of [G.Walker and R.M.W. Wood, Linking first occurrence polynomials over F2 by Steenrod operations, J. Algebra 246 (2001), 739–760] for odd primes p. It is proved that for certain irreducible representations L(λ) of the full matrix semigroup Mn(Fp), the first occurrence of L(λ) as a composition factor in the polynomial algebra P=Fp[x1,,xn] is linked by a Steenrod operation to the first occurrence of L(λ) as a submodule in P. This operation is given explicitly as the image of an admissible monomial in the Steenrod algebra Ap under the canonical anti-automorphism χ. The first occurrences of both kinds are also linked to higher degree occurrences of L(λ) by elements of the Milnor basis of Ap.

Citation

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Phạm Anh Minh. Grant Walker. "Linking first occurrence polynomials over $\mathbb{F}_p$ by Steenrod operations." Algebr. Geom. Topol. 2 (1) 563 - 590, 2002. https://doi.org/10.2140/agt.2002.2.563

Information

Received: 24 January 2002; Accepted: 10 July 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1004.55011
MathSciNet: MR1917067
Digital Object Identifier: 10.2140/agt.2002.2.563

Subjects:
Primary: 55S10
Secondary: 20C20

Rights: Copyright © 2002 Mathematical Sciences Publishers

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