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Andrey Mudrov - One of the best experts on this subject based on the ideXlab platform.
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quantum sphere mathbb s 4 as a non levi conjugacy class
Letters in Mathematical Physics, 2012Co-Authors: Andrey MudrovAbstract:We construct a \({U_\hbar(\mathfrak{sp}(4))}\)-equivariant quantization of the four-dimensional complex sphere \({\mathbb{S}^4}\) regarded as a conjugacy class, Sp(4)/Sp(2) × Sp(2), of a simple complex group with non-Levi Isotropy Subgroup, through an operator realization of the quantum polynomial algebra \({\mathbb{C}_\hbar[\mathbb{S}^4]}\) on a highest weight module of \({U_\hbar(\mathfrak{sp}(4))}\).
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quantum sphere s 4 as a non levi conjugacy class
arXiv: Quantum Algebra, 2011Co-Authors: Andrey MudrovAbstract:We construct a U_h(sp(4))-equivariant quantization of the four-dimensional complex sphere S^4 regarded as a conjugacy class, Sp(4)/Sp(2)x Sp(2), of a simple complex group with non-Levi Isotropy Subgroup, through an operator realization of the quantum polynomial algebra C_h[S^4] on a highest weight module of U_h(sp(4)).
Srinivasan Srimathy - One of the best experts on this subject based on the ideXlab platform.
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Motivic Decomposition of Projective Pseudo-homogeneous Varieties
2017Co-Authors: Srinivasan SrimathyAbstract:Let $G$ be a semi-simple algebraic group over a perfect field $k$. A lot of progress has been made recently in computing the Chow motives of projective $G$-homogenous varieties. When $k$ has positive characteristic, a broader class of $G$-homogeneous varieties appear. These are varieties over which $G$ acts transitively with possibly non-reduced Isotropy Subgroup. In this paper we study these varieties which we call ${\it \mbox{projective pseudo-homogeneous varieties}}$ for $G$ inner type over $k$ and prove that their motives satisfy Rost nilpotence. We also find their motivic decompositions and relate them to the motives of corresponding homogeneous varieties.Comment: Final version as appeared in "Transformation Groups
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Motivic Decomposition of Projective Pseudo-Homogeneous Varieties
'Wiley', 2016Co-Authors: Srinivasan SrimathyAbstract:Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the Isotropy Subgroup at a point on such a variety is a parabolic Subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the Isotropy Subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt
P D Jarvis - One of the best experts on this subject based on the ideXlab platform.
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markov invariants and the Isotropy Subgroup of a quartet tree
Journal of Theoretical Biology, 2009Co-Authors: J G Sumner, P D JarvisAbstract:The purpose of this article is to show how the Isotropy Subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results directly to Markov invariants, thereby extending previous theoretical results by systematically identifying linear combinations that vanish for a given quartet. We also note that the theory is fully generalizable to arbitrary trees and is equally applicable to the related case of phylogenetic invariants. All results follow from elementary consideration of the representation theory of finite groups.
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Markov invariants and the Isotropy Subgroup of a quartet
2008Co-Authors: J G Sumner, P D JarvisAbstract:The purpose of this article is to show how the Isotropy Subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results directly to Markov invariants, thereby extending previous theoretical results by systematically identifying linear combinations that vanish for a given quartet. We also note that the theory is fully generalizable to arbitrary trees and is equally applicable to the related case of phylogenetic invariants. All results follow from elementary consideration of the representation theory of finite groups
Patrão Mauro - One of the best experts on this subject based on the ideXlab platform.
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The Isotropy representation of a real flag manifold : split real forms
'Elsevier BV', 2016Co-Authors: Patrão Mauro, San Martin, Luiz A. B.Abstract:Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We study the Isotropy representation of real flag manifolds associated to simple Lie algebras that are split real forms of complex simple Lie algebras. For each Dynkin diagram the invariant irreducible subspaces for the compact part of the Isotropy Subgroup are described. Contrary to the complex flag manifolds the decomposition into irreducible components is not unique in general. In other words there are cases with infinitely many invariant subspaces. (C) 2015 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.We study the Isotropy representation of real flag manifolds associated to simple Lie algebras that are split real forms of complex simple Lie algebras. For each Dynkin diagram the invariant irreducible subspaces for the compact part of the Isotropy subgro263547579CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [310790/09-3, 303755/09-1]FAPESP [2012/18780-0]CNPq [476024/2012-9]310790/09-3; 303755/09-1; 476024/2012-92012/18780-
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The Isotropy Representation of a Real Flag Manifold: Split Real Forms
2014Co-Authors: Patrão Mauro, Martin, Luiz A. B. SanAbstract:We study the Isotropy representation of real flag manifolds associated to simple Lie algebras that are split real forms of complex simple Lie algebras. For each Dynkin diagram the invariant irreducible subspaces for the compact part of the Isotropy Subgroup are described. Contrary to the complex flag manifolds the decomposition into irreducible components is not in general unique, since there are cases with infinitely many invariant subspaces
Von Schultz Christian - One of the best experts on this subject based on the ideXlab platform.
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Supersymmetric geometries of IIA supergravity II
'Springer Science and Business Media LLC', 2015Co-Authors: Gran Ulf, Papadopoulos G., Von Schultz ChristianAbstract:We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose Isotropy Subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor equations impose some mild constraints on the geometry of the spacetime which include the existence of a time-like Killing vector field which leaves the fields and the Killing spinor invariant
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Supersymmetric geometries of IIA supergravity II
'Springer Science and Business Media LLC', 2015Co-Authors: Gran Ulf, Papadopoulos George, Von Schultz ChristianAbstract:We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose Isotropy Subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor equations impose some mild constraints on the geometry of the spacetime which include the existence of a time-like Killing vector field which leaves the fields and the Killing spinor invariant.Comment: 19 page
