Results 11 to 20 of about 1,001 (48)
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 +2 more
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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
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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
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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
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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
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Feigin–Odesskii brackets associated with Kodaira cycles and positroid varieties
Proceedings of the London Mathematical Society, Volume 130, Issue 5, May 2025.Abstract We establish a link between open positroid varieties in the Grassmannians G(k,n)$G(k,n)$ and certain moduli spaces of complexes of vector bundles over Kodaira cycle Cn$C^n$, using the shifted Poisson structure on the latter moduli spaces and relating them to the standard Poisson structure on G(k,n)$G(k,n)$.
Zheng Hua, Alexander Polishchuk
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Segre products of cluster algebras
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3777-3785, December 2024.Abstract We show that under mild assumptions the Segre product of two graded cluster algebras has a natural cluster algebra structure.
Jan E. Grabowski, Lauren Hindmarch
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Valuative invariants for large classes of matroids
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
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Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 1169-1191, March 2024.Abstract We initiate the study of K$K$‐theory Soergel bimodules, a global and K$K$‐theoretic version of Soergel bimodules. We show that morphisms of K$K$‐theory Soergel bimodules can be described geometrically in terms of equivariant K$K$‐theoretic correspondences between Bott–Samelson varieties.
Jens Niklas Eberhardt
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Maximal disjoint Schubert cycles in rational homogeneous varieties
Mathematische Nachrichten, Volume 297, Issue 1, Page 174-194, January 2024.Abstract In this paper, we study properties of the Chow ring of rational homogeneous varieties of classical type, more concretely, effective zero divisors of low codimension, and a related invariant called effective good divisibility. This information is then used to study the question of (non)existence of nonconstant maps among these varieties ...
Roberto Muñoz +2 more
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