Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2311.13510

Jordan correspondence and block distribution of characters

Radha Kessar·Gunter Malle
View original source ↗Read source document ↗Export metadata ↓

Abstract

We complete the determination of the $\ell$-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the $\ell$-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from $\ell$ has connected centre. As a consequence we derive a compatibility between $\ell$-blocks, $e$-Harish-Chandra series and Jordan decomposition. Further we apply our results to complete the proof of Robinson's conjecture on defects of characters.

Explore related subjects

math.RTmath.GR

Keep this discovery

BibTeXRIS

Radha Kessar, Gunter Malle. 2023-11-22. Jordan correspondence and block distribution of characters. https://arxiv.org/abs/2311.13510

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

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Whittaker supermodules over Lie superalgebras

In this paper, we develop a general theory of quasi-Whittaker supermodules over Lie superalgebras induced from an arbitrary ideal. We determine the quasi-Whittaker vectors in universal supermodules, establish an irreducibility criterion, and classify several families of irreducible supermodules. The odd part produces a new irreducibility phenomenon absent from the Lie algebra setting. As applications, we determine all irreducible quasi-Whittaker supermodules over the $N=1$ super Schr\"odinger algebra and the $N=1$ $\frac{3}{2}$-conformal Galilei superalgebra, and over the complete spectrum-generating superalgebra in a special case.

math.RT↗
arXiv2026

Rankin--Selberg integrals of opposite conductor--one newforms

Let $F$ be a nonarchimedean local field of characteristic zero and let $n\geq2$. For $r=n,n+1$, let $\Pi_r$ be an irreducible tempered representation of ${\rm GL}_r(F)$ of conductor one and with trivial central character. We evaluate the Rankin--Selberg integral of opposite newforms in $\Pi_{n+1}\times \Pi_n$ explicitly and show that its central value is nonzero. As an application, this implies a case of Disegni--Zhang's conjecture on the nonvanishing of local relative characters.

math.RT↗
arXiv2026

Obstructions to Jacobi-Finiteness of Quivers with Potentials

We show that Jacobi-finite potentials need not exist on finite $2$-acyclic quivers. Our main tool is a matrix-valued Golod--Shafarevich--Vinberg inequality for quotients of completed path algebras by finitely many, possibly nonhomogeneous, topological relations. Applied to cyclic derivatives, it yields a potential-dependent obstruction to the finite-dimensionality of completed Jacobian algebras. We then construct a purely quiver-level criterion excluding every Jacobi-finite potential on a given quiver, and exhibit a family of quivers for which every potential has an infinite-dimensional Jacobian algebra.

math.RT↗