Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.08490

The solvable degree of a Schur algebra

Gabriele Nebe·David Schlang
View original source ↗Read source document ↗Export metadata ↓

Abstract

The solvable degree of a Schur algebra $D$ is the greatest common divisor of all integers $n$ such that $D^{n\times n}$ is a direct summand of the rational group algebra $\Q G$ for some finite solvable group $G$. The main result of this paper gives divisibility conditions on the solvable degree depending on the center and the rational primes that divide the discriminant of $D$.

Explore related subjects

math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gabriele Nebe, David Schlang. 2026-10-06. The solvable degree of a Schur algebra. https://arxiv.org/abs/2610.08490

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantum roots for Kac-Moody root systems and finiteness properties of the Kac-Moody affine Bruhat order

Let $G$ be a split Kac-Moody group over a local field. In their study of the Iwahori-Hecke algebra of $G$, A.Braverman, D. Kazhdan and M. Patnaik defined a partial order - called the affine Bruhat order - on the extended affine Weyl semi-group $W^+$ of $G$. In this paper, we study finiteness questions for covers and co-covers of $W^+$, generalizing results of A. Welch. In particular we prove that the intervals for this order are finite. Our results rely on the finiteness of the set of quantum roots of arbitrary Kac-Moody root systems, which we prove. We also obtain a classification of quantum roots.

math.RT↗
arXiv2026

Reductive monoids over general base

We develop a theory of affine algebraic monoids over connected base schemes whose unit groups are split reductive groups. Our main result is a classification theorem for such objects, generalizing the work of Vinberg and Rittatore over a field. As applications, we obtain combinatorial descriptions and normality properties of orbit closures, prove a Steinberg-type theorem on adjoint quotients of split reductive monoids, and construct finite type integral models of the Vinberg monoids.

math.RT↗
arXiv2026

Frobenius functors and $n$-torsionfree objects

We study $n$-torsionfree objects in abelian categories with enough projectives. Frobenius functors preserve $n$-torsionfreeness, and faithful ones reflect it. We prove that stabilization of the torsionfree filtration implies weak Gorensteinness. For Frobenius extensions satisfying a generator condition, we compare the terms of minimal injective resolutions and obtain transfer of Auslander-type conditions and of the Auslander--Gorenstein conjecture. We also compute a family of non-Gorenstein algebras whose torsionfree filtrations stabilize at level two and contain explicit nonprojective Gorenstein projective modules.

math.RT↗