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12
A Proof Of The Mullineux Conjecture
 Math. Z
, 1997
"... Introduction A partition of a positive integer n is a sequence ( 1 2 \Delta \Delta \Delta m ? 0) of integers such that P i = n. For a positive integer p, a partition = ( 1 2 \Delta \Delta \Delta m ) (or its Young diagram) is called pregular if it does not have p or more equal parts, i. ..."
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Introduction A partition of a positive integer n is a sequence ( 1 2 \Delta \Delta \Delta m ? 0) of integers such that P i = n. For a positive integer p, a partition = ( 1 2 \Delta \Delta \Delta m ) (or its Young diagram) is called pregular if it does not have p or more equal parts, i.e. if there does not exist t m \Gamma (p \Gamma 1) with t = t+1 = \Delta \Delta \Delta = t+p\Gamma1 . Let F be a field of characteristic p ? 0. It is well known that ir
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 ..."
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Cited by 30 (1 self)
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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
Extensions Of Modules Over Schur Algebras, Symmetric Groups And Hecke Algebras
, 2000
"... We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite ..."
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Cited by 23 (7 self)
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We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finitedimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.
Direct images of bundles under Frobenius morphism, Invent
 Mathematics Department, University of Arizona, 617 N Santa Rita, Tucson
"... Abstract. Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k) = p> 0 and F: X → X1 be the relative Frobenius morphism. For any vector bundle W on X, we prove that instability of F∗W is bounded by instability of W ⊗ Tℓ (Ω1 X) (0 ≤ ℓ ≤ n(p − 1))(Co ..."
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Abstract. Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k) = p> 0 and F: X → X1 be the relative Frobenius morphism. For any vector bundle W on X, we prove that instability of F∗W is bounded by instability of W ⊗ Tℓ (Ω1 X) (0 ≤ ℓ ≤ n(p − 1))(Corollary 4.9). When X is a smooth projective curve of genus g ≥ 2, it implies F∗W being stable whenever W is stable. Dedicated to Professor Zhexian Wan on the occasion of his 80th birthday. 1.
Galois Representations, Hecke Operators, and the modp Cohomology of GL(3, Z) with Twisted Coefficients
, 1998
"... ..."
On properties of the Mullineux map with an application to Schur modules
, 1999
"... this paper we study a third description of M based on the operator J on the set of pregular partitions defined in [13] ..."
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this paper we study a third description of M based on the operator J on the set of pregular partitions defined in [13]
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
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
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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 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.
HOOK MODULES FOR GENERAL LINEAR GROUPS
, 2008
"... For an arbitrary infinite field k of characteristic p> 0, we describe the structure of a block of the algebraic monoid Mn(k) (all n × n matrices over k), or, equivalently, a block of the Schur algebra S(n, p), whose simple modules are indexed by phook partitions. The result is known; we give an ..."
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For an arbitrary infinite field k of characteristic p> 0, we describe the structure of a block of the algebraic monoid Mn(k) (all n × n matrices over k), or, equivalently, a block of the Schur algebra S(n, p), whose simple modules are indexed by phook partitions. The result is known; we give an elementary and selfcontained proof, based only on a result of Peel and Donkin’s description of the blocks of Schur algebras. The result leads to a character formula for certain simple GLn(k)modules, valid for all n and all p. This character formula is a special case of one found by Brundan, Kleshchev, and Suprunenko and, independently, by Mathieu and Papadopoulo.
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