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Showing 1 to 5 of 5 for “"classical invariant theory"”.
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Computational Algebraic Geometry Applied to Invariant Theory
Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer …
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Classification of second-order conformally-superintegrable systems
… I use this correspondence, and the tools of classical-invariant theory, to determine the inequivalent orbits under this action and show there are only 10 conformal-classes. This answers an open problem by showing that no unknown systems exist on the sphere. Additional interest in these …
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Computational Tradeoffs and Symmetry in Polynomial Nonnegativity
… In the second part, we construct coordinate-invariant sufficient conditions for nonnegativity and study the symmetry properties of the space of Gram matrices. By considering it as a representation of GL(n,R) and combining this module structure with classical invariant theory, we construct an …
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Dual Pairs and Disconnected Reductive Groups
In R. Howe’s seminal paper, “Remarks on classical invariant theory,” he introduces the notion of a Lie algebra dual pair (a pair (g₁, g₂) of reductive Lie subalgebras of a Lie algebra g such that g₁ and g₂ equal each other’s centralizers in g) and the notion of a Lie group dual pair (a pair (G₁, …
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On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution
… this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the …