84 papers
This paper introduces Calabi--Yau quadruples to demonstrate that their associated Higgs categories are -Calabi--Yau Frobenius extriangulated categories with canonical -cluster-tilting subcategories, thereby proving that both relative Amiot--Guo--Keller and Higgs constructions transform silting reduction into Calabi--Yau reduction.
This paper establishes an explicit description of the highest weights and joint highest weight vectors for the irreducible representations of the dual pair and within the supersymmetric algebra , thereby providing a concrete realization of their Howe duality correspondence.
This paper introduces the concept of uniformly dominant local rings, establishes sufficient conditions for their existence in various classes such as Burch rings, and derives upper bounds for the Orlov spectrum of their singularity categories while demonstrating the preservation of this property under basic operations.
This article provides an overview of the Plancherel theory for Riemannian symmetric spaces by demonstrating how Harish-Chandra's theorem can be derived using recently developed methods originally designed for real spherical spaces.
This paper classifies and constructs differential symmetry breaking operators from a line bundle over to a vector bundle over , while determining their factorization identities, the associated branching laws for generalized Verma modules of , and the resulting -representations.
This paper introduces the concept of strongly interlocked modules for vertex operator algebras to establish the well-definedness and key properties of graded pseudo-traces, subsequently applying this framework to fully characterize such modules for rank one Heisenberg and universal Virasoro algebras.
This paper investigates the Rumin differentials within irreducible unitary representations of the (2,3,5) nilpotent Lie group, computing their spectra and zeta-regularized determinants for Schrödinger representations while evaluating the analytic torsion for generic representations.
This paper establishes the existence of superdecomposable pure-injective modules over Jacobian algebras associated with triangulations of closed surfaces (excluding spheres with four or fewer punctures) by demonstrating the presence of independent pairs of dense chains of pointed modules in non-domestic skew-gentle and (skew) Brauer graph algebras, thereby confirming M. Prest's conjecture for these specific cases.
This paper provides an explicit classification of all simple -modules that are torsion-free of rank 1 over the Cartan subalgebra, while also establishing analogous results for the first Weyl algebra and the Lie superalgebra .
This paper establishes the compactness of a character variety classifying continuous group actions on algebraic real hyperbolic spaces of arbitrary dimension, unifying previous compactifications and proving rigidity results for irreducible representations via the introduction of algebraic and abstract cross-ratios.
This paper classifies the finite-dimensional irreducible representations of the restricted super Yangian and the restricted truncated shifted super Yangian associated with the general linear Lie superalgebra over an algebraically closed field of characteristic .
This paper completes the classification of measures on Cameron's elementary treelike Fraïssé classes by establishing a bijection for -colored rooted binary trees that yields infinite families of novel semisimple tensor categories with superexponential growth, while simultaneously proving the nonexistence of such measures on -colored and labeled tree classes for .
This paper proves that the dual canonical bases of Drinfeld double quantum groups coincide with Berenstein–Greenstein's double canonical bases by utilizing the geometry of NKS quiver varieties to reinterpret their algebraic construction, thereby establishing their positivity and invariance under braid group actions.
This paper explicitly computes the images of specific parabolically induced modules, including infinite-dimensional representations like -Verma supermodules, under rank-one Duflo-Serganova functors for general linear Lie superalgebras, thereby extending the understanding of these functors beyond finite-dimensional cases.
This paper verifies the local analogue of Jiang's conjecture regarding the upper bound of geometric wavefront sets for Arthur type representations of split classical -adic groups with large , thereby establishing related upper bound conjectures by combining Waldspurger's endoscopic transfer with recent wavefront set computations.
This paper establishes that the degenerations of cohomological Hall algebras associated with 2-Calabi-Yau categories and preprojective algebras, with respect to the "less perverse" filtration, are isomorphic to the enveloping algebra of the current Lie algebra of the BPS Lie algebra, a result proven at the sheafified level and extended to torus-deformed settings to connect these structures with Maulik-Okounkov Yangians.
This paper characterizes stable equivalences between centralizer matrix algebras over arbitrary fields using a new matrix equivalence relation, demonstrating that such equivalences induce Morita-type stable equivalences that preserve key homological dimensions and validate the Alperin–Auslander/Auslander–Reiten conjecture in this context.
This paper establishes two explicit formulas for counting -points of orbital varieties in ad-nilpotent ideals of type using Hall-Littlewood functions and -weighted tableaux, while providing new proofs and applications for results concerning nilpotent Hessenberg varieties, square-zero matrices, and double coset counts.
This paper introduces a homological stratification theory for rigidly-compactly generated tensor-triangulated categories, demonstrating its robust descent properties to provide a unified framework for answering when stratification descends and extending equivariant module spectrum results from finite groups to compact Lie groups.
This paper classifies deformation quantizations of smooth, admissible symplectic supervarieties by generalizing the Bezrukavnikov-Kaledin result to the super case, establishing a correspondence with their even reduced symplectic varieties, and applying these findings to nilpotent orbits of basic Lie superalgebras.