The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Fernando Szechtman - One of the best experts on this subject based on the ideXlab platform.
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steinberg lattice of the General Linear Group and its modular reduction
Journal of Group Theory, 2011Co-Authors: Fernando SzechtmanAbstract:Let G 1⁄4 GLnðqÞ be the General Linear Group of degree nd 2 defined over a finite field Fq of characteristic p. We fix a prime l0 p and let R denote a local principal ideal domain having characteristic 0, maximal ideal lR, and containing a primitive p-th root of unity. Then the residue field K 1⁄4 R=lR has characteristic l and a primitive p-th root of unity. By a Steinberg lattice of G over R we understand a left RG-module, say M, which is free of rank qnðn 1Þ=2 as an R-module and a¤ords the Steinberg character. The reduction of M modulo l is the KG-module M=lM. In this paper the Steinberg lattice is the left ideal I 1⁄4 RG e of the Group algebra RG,
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Steinberg lattice of the General Linear Group and its modular reduction
arXiv: Representation Theory, 2008Co-Authors: Fernando SzechtmanAbstract:We study the Steinberg lattice of the General Linear Group when reduced modulo a prime different from the defining characteristic.
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MODULAR REDUCTION OF THE STEINBERG LATTICE OF THE General Linear Group
Journal of Algebra and Its Applications, 2008Co-Authors: Fernando SzechtmanAbstract:Each factor of the natural filtration of the modular reduction of the Steinberg representation of the General Linear Group is shown to be completely reducible and the entire modular reduction is shown to be multiplicity free.
Alejandro H Morales - One of the best experts on this subject based on the ideXlab platform.
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rook theory of the finite General Linear Group
Experimental Mathematics, 2020Co-Authors: Joel Brewster Lewis, Alejandro H MoralesAbstract:Matrices over a finite field having fixed rank and restricted support are a natural q-analog of rook placements on a board, even though their enumeration is known to yield nonpolynomial answers in ...
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rook theory of the finite General Linear Group
arXiv: Combinatorics, 2017Co-Authors: Joel Brewster Lewis, Alejandro H MoralesAbstract:Matrices over a finite field having fixed rank and restricted support are a natural $q$-analogue of rook placements on a board. We develop this $q$-rook theory by defining a corresponding analogue of the hit numbers. Using tools from coding theory, we show that these $q$-hit and $q$-rook numbers obey a variety of identities analogous to the classical case. We also explore connections to earlier $q$-analogues of rook theory, as well as settling a polynomiality conjecture and finding a counterexample of a positivity conjecture of the authors and Klein.
Oded Yacobi - One of the best experts on this subject based on the ideXlab platform.
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A quantum analogue of Kostantʼs theorem for the General Linear Group
Journal of Algebra, 2011Co-Authors: Avraham Aizenbud, Oded YacobiAbstract:Abstract A fundamental result in representation theory is Kostantʼs theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the General Linear Group, and from this deduce the analogous result for reflection equation algebras.
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A quantum analogue of Kostant's theorem for the General Linear Group
arXiv: Quantum Algebra, 2010Co-Authors: Avraham Aizenbud, Oded YacobiAbstract:A fundamental result in representation theory is Kostant's theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the General Linear Group, and from this deduce the analogous result for reflection equation algebras.
Seyed Hassan Alavi - One of the best experts on this subject based on the ideXlab platform.
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triple factorisations of the General Linear Group and their associated geometries
Linear Algebra and its Applications, 2015Co-Authors: Seyed Hassan Alavi, John Bamberg, Cheryl E. PraegerAbstract:Abstract Triple factorisations of finite Groups G of the form G = P Q P are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation G = P Q P corresponds to a G-flag transitive point/line geometry such that ‘each pair of points is incident with at least one line’. We call such a geometry colLinearly complete, and duality (interchanging the roles of points and lines) gives rise to the notion of concurrently complete geometries. In this paper, we study triple factorisations of the General Linear Group GL ( V ) as PQP where the subGroups P and Q either fix a subspace or fix a decomposition of V as V 1 ⊕ V 2 with dim ( V 1 ) = dim ( V 2 ) .
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Triple factorisations of the General Linear Group and their associated geometries
arXiv: Group Theory, 2014Co-Authors: Seyed Hassan Alavi, John Bamberg, Cheryl E. PraegerAbstract:Triple factorisations of finite Groups $G$ of the form $G=PQP$ are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation $G=PQP$ corresponds to a $G$-flag transitive point/line geometry such that `each pair of points is incident with at least one line'. We call such a geometry \emph{colLinearly complete}, and duality (interchanging the roles of points and lines) gives rise to the notion of \emph{concurrently complete} geometries. In this paper, we study triple factorisations of the General Linear Group $\mathrm{GL}(V)$ as $PQP$ where the subGroups $P$ and $Q$ either fix a subspace or fix a decomposition of $V$ as $V_1\oplus V_2$ with $\dim(V_{1})=\dim(V_{2})$.
Cheryl E. Praeger - One of the best experts on this subject based on the ideXlab platform.
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triple factorisations of the General Linear Group and their associated geometries
Linear Algebra and its Applications, 2015Co-Authors: Seyed Hassan Alavi, John Bamberg, Cheryl E. PraegerAbstract:Abstract Triple factorisations of finite Groups G of the form G = P Q P are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation G = P Q P corresponds to a G-flag transitive point/line geometry such that ‘each pair of points is incident with at least one line’. We call such a geometry colLinearly complete, and duality (interchanging the roles of points and lines) gives rise to the notion of concurrently complete geometries. In this paper, we study triple factorisations of the General Linear Group GL ( V ) as PQP where the subGroups P and Q either fix a subspace or fix a decomposition of V as V 1 ⊕ V 2 with dim ( V 1 ) = dim ( V 2 ) .
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Triple factorisations of the General Linear Group and their associated geometries
arXiv: Group Theory, 2014Co-Authors: Seyed Hassan Alavi, John Bamberg, Cheryl E. PraegerAbstract:Triple factorisations of finite Groups $G$ of the form $G=PQP$ are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation $G=PQP$ corresponds to a $G$-flag transitive point/line geometry such that `each pair of points is incident with at least one line'. We call such a geometry \emph{colLinearly complete}, and duality (interchanging the roles of points and lines) gives rise to the notion of \emph{concurrently complete} geometries. In this paper, we study triple factorisations of the General Linear Group $\mathrm{GL}(V)$ as $PQP$ where the subGroups $P$ and $Q$ either fix a subspace or fix a decomposition of $V$ as $V_1\oplus V_2$ with $\dim(V_{1})=\dim(V_{2})$.