Tootfinder

A Proof of the Box Conjecture for Commuting Pairs of Matrices
J. Irving, T. Ko\v{s}ir, M. Mastnak
https://arxiv.org/abs/2403.18574 https://

A Proof of the Box Conjecture for Commuting Pairs of Matrices
We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al \cite{IKvSZ}. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the Burge correspondence between the set of all partitions and a set of binary words \cite{Bur-1, Bur-2}. For connection with the algebraic and geometric setup of matrices and orbits we employ some of Shayman's results on invariant subspaces of a nilpotent …

This https://arxiv.org/abs/2310.00477 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On m-tuples of nilpotent 2x2 matrices over an arbitrary field
The algebra of ${\rm GL}_n$-invariants of $m$-tuples of $n\times n$ matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators of polynomial invariants even in case of a pair of $2\times 2$ matrices are not known. Working over an arbitrary field we classified all ${\rm GL}_2$-orbits on $m$-tuples of $2\times 2$ nilpotent matrices for all $m>0$. As a consequence, we obtained a minima…

Whittle Index Based User Association in Dense Millimeter Wave Networks
Mandar R. Nalavade, Gaurav S. Kasbekar, Vivek S. Borkar
https://arxiv.org/abs/2403.09279

Whittle Index Based User Association in Dense Millimeter Wave Networks
We address the problem of user association in a dense millimeter wave (mmWave) network, in which each arriving user brings a file containing a random number of packets and each time slot is divided into multiple mini-slots. This problem is an instance of the restless multi-armed bandit problem, and is provably hard to solve. Using a technique introduced by Whittle, we relax the hard per-stage constraint that each arriving user must be associated with exactly one mmWave base station (mBS) to a l…

This https://arxiv.org/abs/2403.07080 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Kazhdan-Lusztig map and Langlands duality
Let $G$ be a connected reductive group over $\mathbb{C}$ with Weyl group $W$. Following a suggestion of Bezrukavnikov, we define a map from two-sided cells to conjugacy classes in $W$ using the geometry of the affine flag variety. This is an affine analog of the classical story of two-sided cells of $W$, special nilpotent orbits and special representations of $W$. The proof involves studying Springer representations appearing in the cohomology of affine Springer fibers. This relies on tools dev…

This https://arxiv.org/abs/2102.05339 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Formanek-Procesi group with base a right-angled Artin group: Residual nilpotence and Lie algebra
We investigate the Lie algebra of the Formanek-Procesi group FP(H) with base group H a right-angled Artin group. We show that the Lie algebra gr(FP(H)) has a presentation that is dictated by the group presentation. Moreover we show that FP(H) is a Magnus group.

This https://arxiv.org/abs/2202.10812 has been replaced.
link: https://scholar.google.com/scholar?q=a

Anti-associative algebras
An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types of nonassociative algebras, obtained either by the process of polarization, such as Jacobi-Jordan algebras, or obtained by deformation quantization, are associated with this class of algebras. Following Markl-Remms work, we describe the operads associated with…