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Related papers: Web invariants for flamingo Specht modules

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The space of subvarieties of P^n with a fixed Hilbert polynomial is not complete. Grothendieck defined a completion by relaxing "variety" to "scheme", giving the complete_Hilbert scheme_ of subschemes of P^n with fixed Hilbert polynomial.…

Algebraic Geometry · Mathematics 2010-05-02 Valery Alexeev , Allen Knutson

Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…

General Physics · Physics 2020-05-20 R. T. Cavalcanti , J. M. Hoff da Silva

We define an invariant of tangles and framed tangles given a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying natural properties. We give several examples of Reidemeister pairs derived from racks,…

Geometric Topology · Mathematics 2013-01-28 João Faria Martins , Roger Picken

We compare two natural bases for the invariant space of a tensor product of irreducible representations of A_2, or sl(3). One basis is the web basis, defined from a skein theory called the combinatorial A_2 spider. The other basis is the…

q-alg · Mathematics 2007-05-23 Mikhail Khovanov , Greg Kuperberg

We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which…

Machine Learning · Computer Science 2022-10-04 Derek Lim , Joshua Robinson , Lingxiao Zhao , Tess Smidt , Suvrit Sra , Haggai Maron , Stefanie Jegelka

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

Machine Learning · Computer Science 2021-10-28 Jonas A. Actor , Andy Huang , Nathaniel Trask

In this paper we consider the mixed tensor space of a $\mathbb Z_2$-graded vector space. We obtain a spanning set of invariants of the associated symmetric algebra under the action of the general linear supergroup as well as the queer…

Representation Theory · Mathematics 2023-08-29 Santosha Pattanayak , Preena Samuel

We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial complex, and which is explicitly invariant under a group…

Combinatorics · Mathematics 2024-03-05 Gemma De las Cuevas , Matt Hoogsteder Riera , Tim Netzer

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…

Quantum Physics · Physics 2013-11-13 Jacob Biamonte , Ville Bergholm , Marco Lanzagorta

We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…

Algebraic Geometry · Mathematics 2024-02-05 Daniel Halpern-Leistner , Andres Fernandez Herrero , Trevor Jones

Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…

Combinatorics · Mathematics 2020-08-20 Flavia Bonomo-Braberman , Dora Tilli

We present a simplified exposition of some classical and modern results on graph drawings in the plane. These results are chosen so that they illustrate some spectacular recent higher-dimensional results on the border of topology and…

Geometric Topology · Mathematics 2020-12-23 A. Skopenkov

Let $M$ be a smooth projective variety and $\mathbf{D}$ an ample normal crossings divisor. From topological data associated to the pair $(M, \mathbf{D})$, we construct, under assumptions on Gromov-Witten invariants, a series of…

Symplectic Geometry · Mathematics 2021-02-24 Sheel Ganatra , Daniel Pomerleano

We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and web bases, which answers Rhoades's question.…

Combinatorics · Mathematics 2021-10-19 Byung-Hak Hwang , Jihyeug Jang , Jaeseong Oh

Let $R$ be the homogeneous coordinate ring of the Grassmannian $\mathbb{G}=\operatorname{Gr}(2,n)$ defined over an algebraically closed field of characteristic $p>0$. In this paper we give a completely characteristic free description of the…

Algebraic Geometry · Mathematics 2017-06-19 Theo Raedschelders , Špela Špenko , Michel Van den Bergh

In 2022 Kim showed when a graph $G$ is ternary (without induced cycles of length divisible by three), its independence complex $\text{Ind}(G)$ is either contractible or homotopy equivalent to a sphere. In this paper, we show that when…

Combinatorics · Mathematics 2025-09-29 Margaret Bayer , Richard Danner , Thiago Holleben , Marie Kramer , Yirong Yang

Univariate polynomials are called stable with respect to a domain $D$ if all of their roots lie in $D$. We study linear slices of the space of stable univariate polynomials with respect to a half-plane. We show that a linear slice always…

Algebraic Geometry · Mathematics 2025-08-07 Sebastian Debus , Cordian Riener , Robin Schabert

We study maps from a 2D world-sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area preserving…

High Energy Physics - Theory · Physics 2019-08-15 O. Ganor , J. Sonnenschein , S. Yankielowicz

Though algebraic geometry over $\mathbb C$ is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the $n\times n\times n$…

Algebraic Geometry · Mathematics 2012-11-16 Elizabeth S. Allman , Peter D. Jarvis , John A. Rhodes , Jeremy G. Sumner

It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the…

High Energy Physics - Theory · Physics 2009-10-28 Jean-Bernard Zuber
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