linear subspace
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2022 ◽  
Vol 28 (2) ◽  
C. Bowman ◽  
E. Norton ◽  
J. Simental

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.

Żywilla Fechner ◽  
Eszter Gselmann ◽  
László Székelyhidi

AbstractThe purpose of this paper is to prove that if on a commutative hypergroup an exponential monomial has the property that the linear subspace of all sine functions in its variety is one dimensional, then this exponential monomial is a linear combination of generalized moment functions.

2021 ◽  
pp. 50-55
Adrian Tanasa

The Jacobian Conjecture states that any complex n-dimensional locally invertible polynomial system is globally invertible with polynomial inverse. In 1982, Bass et al. proved an important reduction theorem stating that the conjecture is true for any degree of the polynomial system if it is true in degree three. This degree reduction is obtained with the price of increasing the dimension n. We show in this chapter a result concerning partial elimination of variables, which implies a reduction of the generic case to the quadratic one. The price to pay is the introduction of a supplementary parameter 0≤n′≤n, parameter which represents the dimension of a linear subspace where some particular conditions on the system must hold. We exhibit a proof, in a QFT formulation, using the intermediate field method exposed in Chapter 3.

Giorgio Ottaviani ◽  
Zahra Shahidi

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.

Andrei Valerianovich Pavlov

In the article we consider a new scalar production in the linear subspace of n vectors (by analogy with the geometry of Lobachevsky, all two vectors are orthogonal as projections of the third vector). With help of the production we obtain a new form of linear projection of the additional vector to the subspace. The rapid algorithm of finding of optimum linear estimation of additional vector on the known vectors ensues from the projection.

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