Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1902.06668

Asymptotic Hecke algebras and Lusztig-Vogan bijection via affine matrix-ball construction

Dongkwan Kim·Pavlo Pylyavskyy
View original source ↗Read source document ↗Export metadata ↓

Abstract

Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished (or Duflo) involution in each Kazhdan-Lusztig cell of affine symmetric groups. We then use AMBC to give the first known canonical presentation for the asymptotic Hecke algebras of extended affine symmetric groups. As an application, we show that AMBC gives a conceptual way to compute Lusztig-Vogan bijection. For the latter we build upon prior works of Achar and Rush.

Explore related subjects

math.RTmath.CO

Keep this discovery

BibTeXRIS

Dongkwan Kim, Pavlo Pylyavskyy. 2019-02-18. Asymptotic Hecke algebras and Lusztig-Vogan bijection via affine matrix-ball construction. https://arxiv.org/abs/1902.06668

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↗