The Experts below are selected from a list of 4950 Experts worldwide ranked by ideXlab platform
Yuri Bazlov - One of the best experts on this subject based on the ideXlab platform.
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graded multiplicities in the Exterior Algebra
Advances in Mathematics, 2001Co-Authors: Yuri BazlovAbstract:Abstract This paper deals with the graded multiplicities of the “smallest” irreducible representations of a simple Lie Algebra in its Exterior Algebra. An explicit formula for the graded multiplicity of the adjoint representation in terms of the Weyl group exponents was conjectured by A. Joseph; a proof of this conjecture, based on the properties of Macdonald polynomials, is given in the present paper. The same method allows us to calculate the multiplicity of the simple module with highest weight equal to the short dominant root.
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graded multiplicities in the Exterior Algebra
arXiv: Representation Theory, 2000Co-Authors: Yuri BazlovAbstract:We know the multiplicity of the adjoint representation of a semisimple Lie Algebra in its own Exterior Algebra, but how do its copies distribute themselves between the Exterior powers? The answer (the graded multiplicity) is obtained with the aid of Macdonald polynomials.
Claudio Procesi - One of the best experts on this subject based on the ideXlab platform.
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the adjoint representation inside the Exterior Algebra of a simple lie Algebra
Advances in Mathematics, 2015Co-Authors: Corrado De Concini, Paolo Papi, Claudio ProcesiAbstract:Abstract For a simple complex Lie Algebra g we study the space of invariants A = ( ⋀ g ⁎ ⊗ g ⁎ ) g , which describes the isotypic component of type g in ⋀ g ⁎ , as a module over the Algebra of invariants ( ⋀ g ⁎ ) g . As main result we prove that A is a free module, of rank twice the rank of g , over the Exterior Algebra generated by all primitive invariants in ( ⋀ g ⁎ ) g , with the exception of the one of highest degree.
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on special covariants in the Exterior Algebra of a simple lie Algebra
arXiv: Representation Theory, 2014Co-Authors: Corrado De Concini, Paolo Papi, Pierluigi Moseneder Frajria, Claudio ProcesiAbstract:We study the subspace of the Exterior Algebra of a simple complex Lie Algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie Algebra of traceless matrices, by the copies of the n-th symmetric power of the defining representation. As main result we prove that this subspace is a free module over the subAlgebra of the Exterior Algebra generated by all primitive invariants except the one of highest degree.
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the adjoint representation inside the Exterior Algebra of a simple lie Algebra
arXiv: Representation Theory, 2013Co-Authors: Corrado De Concini, Paolo Papi, Claudio ProcesiAbstract:For a simple complex Lie Algebra $\mathfrak g$ we study the space of invariants $A=\left( \bigwedge \mathfrak g^*\otimes\mathfrak g^*\right)^{\mathfrak g}$, (which describes the isotypic component of type $\mathfrak g$ in $ \bigwedge \mathfrak g^*$) as a module over the Algebra of invariants $\left(\bigwedge \mathfrak g^*\right)^{\mathfrak g}$. As main result we prove that $A$ is a free module, of rank twice the rank of $\mathfrak g$, over the Exterior Algebra generated by all primitive invariants in $(\bigwedge \mathfrak g^*)^{\mathfrak g}$, with the exception of the one of highest degree.
Marilena Crupi - One of the best experts on this subject based on the ideXlab platform.
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hilbert functions of graded modules over an Exterior Algebra an algorithmic approach
International Electronic Journal of Algebra, 2020Co-Authors: Luca Amata, Marilena CrupiAbstract:Let $K$ be a field, $E$ the Exterior Algebra of a finite dimensional $K$-vector space, and $F$ a finitely generated graded free $E$-module with homogeneous basis $g_1, \ldots, g_r$ such that $\deg g_1 \le \deg g_2 \le \cdots \le \deg g_r$. Given the Hilbert function of a graded $E$--module of the type $F/M$, with $M$ graded submodule of $F$, the existence of the unique lexicographic submodule of $F$ with the same Hilbert function as $M$ is proved by a new algorithmic approach. Such an approach allows us to establish a criterion for determining if a sequence of nonnegative integers defines the Hilbert function of a quotient of a free $E$--module only via the combinatorial Kruskal--Katona's theorem.
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minimal resolutions of graded modules over an Exterior Algebra
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche Matematiche e Naturali, 2019Co-Authors: Luca Amata, Marilena CrupiAbstract:Let K be a field, E the Exterior Algebra of a n --dimensional K -vector space V . We study projective and injective resolutions over E . More precisely, given a category M of finitely generated Z-graded left and right E -modules, we give upper bounds for the graded Betti numbers and the graded Bass numbers of classes of modules in M .
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bounding betti numbers of monomial ideals in the Exterior Algebra
Pure and Applied Mathematics Quarterly, 2015Co-Authors: Marilena Crupi, Carmela FerroAbstract:Let $K$ be a field, $V$ a $K$-vector space with basis $e_1,\ldots,e_n$, and $E$ the Exterior Algebra of $V$. To a given monomial ideal $I\subsetneq E$ we associate a special monomial ideal $J$ with generators in the same degrees as those of $I$ and such that the number of the minimal monomial generators in each degree of $I$ and $J$ coincide. We call $J$ the colexsegment ideal associated to $I$. We prove that the class of strongly stable ideals in $E$ generated in one degree satisfies the colex lower bound, that is, the total Betti numbers of the colexsegment ideal associated to a strongly stable ideal $I\subsetneq E$ generated in one degree are smaller than or equal to those of $I$.
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hilbert functions and betti numbers of reverse lexicographic ideals in the Exterior Algebra
Turkish Journal of Mathematics, 2012Co-Authors: Marilena Crupi, Carmela FerroAbstract:Let K be a field, V a K-vector space with basis e1,...,en and let E be the Exterior Algebra of V. We study the class of reverse lexicographic ideals in E. We analyze the behaviour of their Hilbert functions and Betti numbers.
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classes of graded ideals with given data in the Exterior Algebra
Communications in Algebra, 2007Co-Authors: Marilena Crupi, Rosanna UtanoAbstract:Let ℱ be the family of graded ideals J in the Exterior Algebra E of a n-dimensional vector space over a field K such that e(E/J) = dim K (E/J) = e, indeg(E/J) = i and H E/J (i) = dim K (E/J) i are fixed integers. It is shown that there exists a unique lexsegment graded ideal J(n, e, i) ∊ ℱ whose Betti numbers give an upper bound for the Betti numbers of the ideals of ℱ. The authors continue the computation of upper bounds for the Betti numbers of graded ideals with given data started in Crupi and Utano (1999).
Corrado De Concini - One of the best experts on this subject based on the ideXlab platform.
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the adjoint representation inside the Exterior Algebra of a simple lie Algebra
Advances in Mathematics, 2015Co-Authors: Corrado De Concini, Paolo Papi, Claudio ProcesiAbstract:Abstract For a simple complex Lie Algebra g we study the space of invariants A = ( ⋀ g ⁎ ⊗ g ⁎ ) g , which describes the isotypic component of type g in ⋀ g ⁎ , as a module over the Algebra of invariants ( ⋀ g ⁎ ) g . As main result we prove that A is a free module, of rank twice the rank of g , over the Exterior Algebra generated by all primitive invariants in ( ⋀ g ⁎ ) g , with the exception of the one of highest degree.
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on special covariants in the Exterior Algebra of a simple lie Algebra
arXiv: Representation Theory, 2014Co-Authors: Corrado De Concini, Paolo Papi, Pierluigi Moseneder Frajria, Claudio ProcesiAbstract:We study the subspace of the Exterior Algebra of a simple complex Lie Algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie Algebra of traceless matrices, by the copies of the n-th symmetric power of the defining representation. As main result we prove that this subspace is a free module over the subAlgebra of the Exterior Algebra generated by all primitive invariants except the one of highest degree.
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the adjoint representation inside the Exterior Algebra of a simple lie Algebra
arXiv: Representation Theory, 2013Co-Authors: Corrado De Concini, Paolo Papi, Claudio ProcesiAbstract:For a simple complex Lie Algebra $\mathfrak g$ we study the space of invariants $A=\left( \bigwedge \mathfrak g^*\otimes\mathfrak g^*\right)^{\mathfrak g}$, (which describes the isotypic component of type $\mathfrak g$ in $ \bigwedge \mathfrak g^*$) as a module over the Algebra of invariants $\left(\bigwedge \mathfrak g^*\right)^{\mathfrak g}$. As main result we prove that $A$ is a free module, of rank twice the rank of $\mathfrak g$, over the Exterior Algebra generated by all primitive invariants in $(\bigwedge \mathfrak g^*)^{\mathfrak g}$, with the exception of the one of highest degree.
Hua Xiuyin - One of the best experts on this subject based on the ideXlab platform.
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homogeneous rota baxter operators on Exterior Algebra in 2 variables
Journal of Natural Science of Heilongjiang University, 2014Co-Authors: Hua XiuyinAbstract:Let F be an Algebraic closed field of characteristic p≠2. In allusion to the question of the Rota-Baxter operators of Exterior Algebra Λ( 2) in two variables over F,by means of calculationg actions of Rota-Baxter operators on the base of Λ( 2),the even Rota-Baxter operators and odd Rota-Baxter operators of Λ( 2) are determined. Furthermore,all homogeneous Rota-Baxter operators of Exterior Algebra Λ( 2) are determined.
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rota baxter operators on Exterior Algebra
Journal of Harbin University of Science and Technology, 2013Co-Authors: Hua XiuyinAbstract:The question of the Rota-Baxter operators of Exterior Algebra Λ( 2) over Fin 2 variables is considered,whereFis an Algebraic closed field of characteristic p≠2. By means of calculationg actions of Rota-Baxter operators on the base of Λ( 2),the Rota-Baxter operators of Λ( 2) are got,further,homomorphic and isomorphisms Rota-Baxter operators of Λ( 2) are determined.
