Results 11 to 20 of about 400 (65)

Airy sheaves for reductive groups

Proceedings of the London Mathematical Society, Volume 126, Issue 1, Page 390-428, January 2023., 2023
Abstract We construct a class of ℓ$\ell$‐adic local systems on A1$\mathbb {A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These sheaves are finite field analogues of generalizations of the classical Airy equation y′′(z)=zy(z)$y^{\prime \prime }(z)=zy(z)$. We employ the geometric Langlands correspondence to construct the
Konstantin Jakob, Masoud Kamgarpour, Lingfei Yi   +2 more
wiley   +1 more source

Singular Rouquier complexes

Proceedings of the London Mathematical Society, Volume 125, Issue 6, Page 1332-1352, December 2022., 2022
Abstract We generalize the construction of Rouquier complexes to the setting of one‐sided singular Soergel bimodules. Singular Rouquier complexes are defined by taking minimal complexes of restricted Rouquier complexes. We show that they retain many of the properties of ordinary Rouquier complexes: they are Δ$\Delta$‐split, they satisfy a vanishing ...
Leonardo Patimo
wiley   +1 more source

Symplectic resolutions, symplectic duality, and Coulomb branches

Bulletin of the London Mathematical Society, Volume 54, Issue 5, Page 1515-1551, October 2022., 2022
Abstract Symplectic resolutions are an exciting new frontier of research in representation theory. One of the most fascinating aspects of this study is symplectic duality: the observation that these resolutions come in pairs with matching properties. The Coulomb branch construction allows us to produce and study many of these dual pairs.
Joel Kamnitzer
wiley   +1 more source

Domains of discontinuity in oriented flag manifolds

Journal of the London Mathematical Society, Volume 106, Issue 2, Page 1380-1442, September 2022., 2022
Abstract We study actions of discrete subgroups Γ$\Gamma$ of semi‐simple Lie groups G$G$ on associated oriented flag manifolds. These are quotients G/P$G/P$, where the subgroup P$P$ lies between a parabolic subgroup and its identity component. For Anosov subgroups Γ⊂G$\Gamma \subset G$, we identify domains in oriented flag manifolds by removing a set ...
Florian Stecker, Nicolaus Treib
wiley   +1 more source

Smooth Schubert varieties in the affine flag variety of type à [PDF]

European journal of combinatorics (Print), 2017
We show that every smooth Schubert variety of affine type A is an iterated fibre bundle of Grassmannians, extending an analogous result by Ryan and Wolper for Schubert varieties of finite type A . As a consequence, we finish a conjecture of Billey–Crites
Edward Richmond, William Slofstra
semanticscholar   +1 more source

Schubert line defects in 3d GLSMs. Part I. Complete flag manifolds and quantum Grothendieck polynomials [PDF]

Journal of High Energy Physics
We construct new half-BPS line defects in 3d N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin ...
Cyril Closset, Wei Gu, Osama Khlaif, E. Sharpe, Hao Zhang, Hao Zou   +5 more
semanticscholar   +1 more source

Schubert line defects in 3d GLSMs. Part II. Partial flag manifolds and parabolic quantum polynomials [PDF]

Journal of High Energy Physics
We construct Schubert line defects in the 3d N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin ...
Cyril Closset, Wei Gu, Osama Khlaif, E. Sharpe, Hao Zhang, Hao Zou   +5 more
semanticscholar   +1 more source

Graded quantum cluster algebras and an application to quantum Grassmannians

Proceedings of the London Mathematical Society, Volume 109, Issue 3, Page 697-732, September 2014., 2014
We introduce a framework for Z‐gradings on cluster algebras (and their quantum analogues) that are compatible with mutation. To do this, one chooses the degrees of the (quantum) cluster variables in an initial seed subject to a compatibility with the initial exchange matrix, and then one extends this to all cluster variables by mutation.
Jan E. Grabowski, Stéphane Launois
wiley   +1 more source

Local cohomology with support in Schubert varieties [PDF]

Compositio Mathematica
This paper is concerned with local cohomology sheaves on generalized flag varieties supported in closed Schubert varieties, which carry natural structures as (mixed Hodge) A black, stylized uppercase letter ‘D’ in a decorative serif/calligraphic font on ...
Michael Perlman
semanticscholar   +1 more source

Desingularizations of Schubert varieties in double Grassmannians [PDF]

, 2006
Let X = Gr(k, V) × Gr(l, V) be the direct product of two Grassmann varieties of k-and l-planes in a finite-dimensional vector space V, and let B ⊂ GL(V) be the isotropy group of a complete flag in V.
E. Smirnov
semanticscholar   +1 more source