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Problems in the Steenrod algebra
 Bull. London Math. Soc
, 1998
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development ..."
Abstract

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This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below. Contents 1 Historical background 4
Galois Representations, Hecke Operators, and the modp Cohomology of GL(3, Z) with Twisted Coefficients
, 1998
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ATG Linking first occurrence polynomials over Fp by Steenrod operations
, 2002
"... Abstract This paper provides analogues of the results of [16] 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 Steenro ..."
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Abstract This paper provides analogues of the results of [16] 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 antiautomorphism 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. AMS Classification 55S10; 20C20
THE GLn(q)MODULE STRUCTURE OF THE SYMMETRIC ALGEBRA AROUND THE STEINBERG MODULE
"... Abstract. We determine the graded composition multiplicity in the symmetric algebra S • (V) of the natural GLn(q)module V, or equivalently in the coinvariant algebra of V, for a large class of irreducible modules around the Steinberg module. This was built on a computation, via connections to algeb ..."
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Abstract. We determine the graded composition multiplicity in the symmetric algebra S • (V) of the natural GLn(q)module V, or equivalently in the coinvariant algebra of V, for a large class of irreducible modules around the Steinberg module. This was built on a computation, via connections to algebraic groups, of the Steinberg module multiplicity in a tensor product of S • (V) with other tensor spaces of fundamental weight modules. 1.
Contents
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may nd of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of ..."
Abstract
 Add to MetaCart
This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may nd of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below.
Linking rst occurrence polynomials over Fp by Steenrod operations
"... Abstract This paper provides analogues of the results of [16] for odd primes p. It is proved that for certain irreducible representations L() of the full matrix semigroup Mn(Fp), the rst occurrence of L() as a composition factor in the polynomial algebra P = Fp[x1; : : : ; xn] is linked by a Steenro ..."
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Abstract This paper provides analogues of the results of [16] for odd primes p. It is proved that for certain irreducible representations L() of the full matrix semigroup Mn(Fp), the rst occurrence of L() as a composition factor in the polynomial algebra P = Fp[x1; : : : ; xn] is linked by a Steenrod operation to the rst occurrence of L() 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 antiautomorphism . The rst occurrences of both kinds are also linked to higher degree occurrences of L() by elements of the Milnor basis of Ap. AMS Classication 55S10; 20C20
general linear group GLn(F2) and the Poincare
"... and conjectures about the modular representation theory of the ..."
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