The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Ernesto Vallejo - One of the best experts on this subject based on the ideXlab platform.
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kronecker products characters partitions and the tensor square conjectures
Advances in Mathematics, 2016Co-Authors: Igor Pak, Greta Panova, Ernesto VallejoAbstract:Abstract We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S n contain all Irreducibles as their constituents. Our main result is that for sufficiently large n they contain representations corresponding to Young diagrams of hooks, two row and diagrams obtained from hooks and two rows by adding a finite number of squares. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and apply this tool using combinatorics of rim hook tableaux in combination with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of S n .
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kronecker products characters partitions and the tensor square conjectures
arXiv: Combinatorics, 2013Co-Authors: Igor Pak, Greta Panova, Ernesto VallejoAbstract:We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S_n contain all Irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and use combinatorics of rim hook tableaux combined with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of S_n.
Igor Pak - One of the best experts on this subject based on the ideXlab platform.
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kronecker products characters partitions and the tensor square conjectures
Advances in Mathematics, 2016Co-Authors: Igor Pak, Greta Panova, Ernesto VallejoAbstract:Abstract We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S n contain all Irreducibles as their constituents. Our main result is that for sufficiently large n they contain representations corresponding to Young diagrams of hooks, two row and diagrams obtained from hooks and two rows by adding a finite number of squares. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and apply this tool using combinatorics of rim hook tableaux in combination with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of S n .
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kronecker products characters partitions and the tensor square conjectures
arXiv: Combinatorics, 2013Co-Authors: Igor Pak, Greta Panova, Ernesto VallejoAbstract:We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S_n contain all Irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and use combinatorics of rim hook tableaux combined with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of S_n.
Martha Precup - One of the best experts on this subject based on the ideXlab platform.
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The singular locus of semisimple Hessenberg varieties
Journal of Algebra, 2019Co-Authors: Erik Insko, Martha PrecupAbstract:Abstract Although regular semisimple Hessenberg varieties are smooth and irreducible, semisimple Hessenberg varieties are not necessarily smooth in general. In this paper we determine the irreducible components of semisimple Hessenberg varieties corresponding to the standard Hessenberg space in all Lie types. We prove that these irreducible components are smooth and give an explicit description of their intersections, which constitute the singular locus. We conclude with an example of a semisimple Hessenberg variety corresponding to another Hessenberg space which is singular and irreducible, showing that results of this nature do not hold for all semisimple Hessenberg varieties.
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The singular locus of semisimple Hessenberg varieties
arXiv: Algebraic Geometry, 2017Co-Authors: Erik Insko, Martha PrecupAbstract:Although regular semisimple Hessenberg varieties are smooth and irreducible, semisimple Hessenberg varieties are not necessarily smooth in general. In this paper we determine the irreducible components of semisimple Hessenberg varieties corresponding to the standard Hessenberg space. We prove that these irreducible components are smooth and give an explicit description of their intersections, which constitute the singular locus. We conclude with an example of a semisimple Hessenberg variety corresponding to another Hessenberg space which is singular and irreducible, showing that results of this nature do not hold for all semisimple Hessenberg varieties.
Greta Panova - One of the best experts on this subject based on the ideXlab platform.
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kronecker products characters partitions and the tensor square conjectures
Advances in Mathematics, 2016Co-Authors: Igor Pak, Greta Panova, Ernesto VallejoAbstract:Abstract We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S n contain all Irreducibles as their constituents. Our main result is that for sufficiently large n they contain representations corresponding to Young diagrams of hooks, two row and diagrams obtained from hooks and two rows by adding a finite number of squares. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and apply this tool using combinatorics of rim hook tableaux in combination with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of S n .
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kronecker products characters partitions and the tensor square conjectures
arXiv: Combinatorics, 2013Co-Authors: Igor Pak, Greta Panova, Ernesto VallejoAbstract:We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S_n contain all Irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and use combinatorics of rim hook tableaux combined with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of S_n.
Sarah Nakato - One of the best experts on this subject based on the ideXlab platform.
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a graph theoretic criterion for absolute irreducibility of integer valued polynomials with square free denominator
Communications in Algebra, 2020Co-Authors: Sophie Frisch, Sarah NakatoAbstract:An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into Irreducibles. In the case of the ring Int(D)={f...
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a graph theoretic criterion for absolute irreducibility of integer valued polynomials with square free denominator
arXiv: Commutative Algebra, 2019Co-Authors: Sophie Frisch, Sarah NakatoAbstract:An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into Irreducibles. In the case of the ring $\text{Int}(D)=\{f\in K[x]\mid f(D)\subseteq D\}$, of integer-valued polynomials on a principal ideal domain $D$ with quotient field $K$, we give an easy to verify graph-theoretic sufficient condition for an element to be absolutely irreducible and show a partial converse: the condition is necessary and sufficient for polynomials with square-free denominator.