Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Eggermont, Rob"'
We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence we obtain that half-spin varieties, which we introduce, are defined by the pullback of equations at a finite l
Externí odkaz:
http://arxiv.org/abs/2403.10274
There are many notions of rank in multilinear algebra: tensor rank, partition rank, slice rank, and strength (or Schmidt rank) are a few examples. Typically the rank $\le r$ locus is not Zariski closed, and understanding the closure (the locus with "
Externí odkaz:
http://arxiv.org/abs/2305.19866
Let $X$ be an affine scheme of $k \times \mathbb{N}$-matrices and $Y$ be an affine scheme of $\mathbb{N} \times \cdots \times \mathbb{N}$-dimensional tensors. The group Sym$(\mathbb{N})$ acts naturally on both $X$ and $Y$ and on their coordinate ring
Externí odkaz:
http://arxiv.org/abs/2212.12458
Much recent literature concerns finiteness properties of infinite-dimensional algebraic varieties equipped with an action of the infinite symmetric group, or of the infinite general linear group. In this paper, we study a common generalisation in whi
Externí odkaz:
http://arxiv.org/abs/2212.05790
A function $f: \mathbb{Z} \to \mathbb{Q}^n$ is a $c$-quasihomomorphism if the Hamming distance between $f(x+y)$ and $f(x)+f(y)$ is at most $c$ for all $x,y \in \mathbb{Z}$. We show that any $c$-quasihomomorphism has distance at most some constant $C(
Externí odkaz:
http://arxiv.org/abs/2204.08392
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used to study a
Externí odkaz:
http://arxiv.org/abs/2105.12621
Publikováno v:
Vietnam J. Math. 50 (2022), pp. 557-580
A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using e
Externí odkaz:
http://arxiv.org/abs/2105.00016
We show that if X_n is a variety of cxn-matrices that is stable under the group Sym([n]) of column permutations and if forgetting the last column maps X_n into X_{n-1}, then the number of Sym([n])-orbits on irreducible components of X_n is a quasipol
Externí odkaz:
http://arxiv.org/abs/2103.05415
Publikováno v:
Commun. Contemp. Math. 21 (2019), no. 7, 1850062
Notions of rank abound in the literature on tensor decomposition. We prove that strength, recently introduced for homogeneous polynomials by Ananyan-Hochster in their proof of Stillman's conjecture and generalised here to other tensors, is universal
Externí odkaz:
http://arxiv.org/abs/1805.01816
Autor:
Eggermont, Rob H., Snowden, Andrew
Draisma recently proved that polynomial representations of $\mathbf{GL}_{\infty}$ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1708.06420