Representation stability for families of linear subspace arrangements

AbstractWe provide a homological construction of unitary simple modules of Cherednik and Hecke algebras of type A via BGG resolutions, solving a conjecture of Berkesch–Griffeth–Sam. We vastly generalize the conjecture and its solution to cyclotomic Cherednik and Hecke algebras over arbitrary ground fields, and calculate the Betti numbers and Castelnuovo–Mumford regularity of certain symmetric linear subspace arrangements.

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Representation stability on the cohomology of complements of subspace arrangements

Algebraic Combinatorics ◽

10.5802/alco.60 ◽

2019 ◽

Vol 2 (4) ◽

pp. 603-611

Author(s):

Artur Rapp

Keyword(s):

Subspace Arrangements ◽

Representation Stability

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Tensors with eigenvectors in a given subspace

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-021-00600-2 ◽

2021 ◽

Author(s):

Giorgio Ottaviani ◽

Zahra Shahidi

Keyword(s):

Algebraic Geometry ◽

Linear Subspace ◽

Chern Classes ◽

Symmetric Tensors

AbstractThe first author with B. Sturmfels studied in [16] the variety of matrices with eigenvectors in a given linear subspace, called the Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the Kalman variety and computing its codimension and degree. Furthermore, we consider the Kalman variety of tensors having singular t-tuples with the first component in a given linear subspace and we prove analogous results, which are new even in the case of matrices. Main techniques come from Algebraic Geometry, using Chern classes for enumerative computations.

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Some properties of D-weak operator topology

Mathematica Slovaca ◽

10.1515/ms-2017-0388 ◽

2020 ◽

Vol 70 (3) ◽

pp. 753-758

Author(s):

Marcel Polakovič

Keyword(s):

Hilbert Space ◽

Effect Algebra ◽

Linear Subspace ◽

Linear Operators ◽

Positive Linear Operators ◽

Weak Operator Topology ◽

Generalized Effect Algebra ◽

Weak Operator ◽

Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

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Hilbert functions and applications to the estimation of subspace arrangements

Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 ◽

10.1109/iccv.2005.114 ◽

2005 ◽

Cited By ~ 3

Author(s):

A.Y. Yang ◽

S. Rao ◽

A. Wagner ◽

Yi Ma ◽

R.M. Fossum

Keyword(s):

Hilbert Functions ◽

Subspace Arrangements

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On projected thick sections of stationary point processes and Boolean models

Advances in Applied Probability ◽

10.2307/1428046 ◽

1996 ◽

Vol 28 (2) ◽

pp. 335-335

Author(s):

Markus Kiderlen

Keyword(s):

Point Process ◽

Stationary Point ◽

Point Processes ◽

Linear Subspace ◽

Isotropic Case ◽

Thick Section ◽

Boolean Models ◽

Dimensional Linear Subspace ◽

Stationary Point Process ◽

Stationary Point Processes

For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

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