Displaying similar documents to “Invariants of four subspaces”

On classical invariant theory and binary cubics

Gerald W. Schwarz (1987)

Annales de l'institut Fourier

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Let G be a reductive complex algebraic group, and let C [ m V ] G denote the algebra of invariant polynomial functions on the direct sum of m copies of the representations space V of G . There is a smallest integer n = n ( V ) such that generators and relations of C [ m V ] G can be obtained from those of C [ n V ] G by polarization and restitution for all m > n . We bound and the degrees of generators and relations of C [ n V ] G , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics. ...

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

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We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.

Link invariants from finite racks

Sam Nelson (2014)

Fundamenta Mathematicae

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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.

On deformation method in invariant theory

Dmitri Panyushev (1997)

Annales de l'institut Fourier

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In this paper we relate the deformation method in invariant theory to spherical subgroups. Let G be a reductive group, Z an affine G -variety and H ⊂ G a spherical subgroup. We show that whenever G / H is affine and its semigroup of weights is saturated, the algebra of H -invariant regular functions on Z has a G -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of G . The deformation method in its usual form,...