84 papers
This paper establishes that a broad class of non-abelian monoidal categories can be realized as subcategories of tilting objects within abelian highest weight categories by utilizing a monoidal enhancement of semi-infinite Ringel duality, a framework that further yields monoidal structures on representations of affine Lie algebras at positive levels.
This paper defines a compactification of the parameter space for the quantum multiplication of hypertoric varieties, following deConcini and Gaiffi, and demonstrates how to extend this multiplication to the compactified space.
This paper classifies intermediate t-structures on the local derived category of a 3-fold flopping contraction and minimal resolutions of Kleinian singularities, thereby describing the complete lattice of torsion classes for associated modification and preprojective algebras and providing foundational steps for understanding spherical objects in derived categories of surfaces and 3-folds.
This paper investigates which four-dimensional real Lie superalgebras, as classified by Backhouse, can be realized as Lagrangian extensions and analyzes their left-symmetric structures, finding that all but two of them are Novikov superalgebras.
This paper initiates a systematic study of modular representations of symmetric groups arising from braiding in tensor categories over fields of positive characteristic, establishing their equivalence to the classification of polynomial functors and the extension of strict polynomial functors to arbitrary tensor categories.
This paper introduces the -TF equivalence for objects in an abelian length category to coarsen the standard TF equivalence, demonstrating that the resulting structure forms a finite, complete rational generalized fan in the dual real Grothendieck group that corresponds to the normal fan of the object's Newton polytope.
This paper classifies irreducible covariant representations of algebraic affine group actions on affine varieties by adapting the Mackey machine to the algebraic setting and demonstrates applications to continuous representations of motion groups on Banach spaces.
This paper constructs new infinite families of Ramanujan complexes with distinct local structures by utilizing super-definite unitary groups over totally real number fields, yielding novel examples across various types and providing a fully explicit rank-5 construction that generates golden gates for the real Lie group .
This paper proves that the star product for quantum symmetric pair coideal subalgebras is short, a result the authors use to provide new, elementary proofs of fundamental properties such as the existence of the bar involution and the intertwiner property of the quasi K-matrix without relying on the quasi K-matrix itself.
This paper constructs a new class of simple weight modules for the twisted Heisenberg-Virasoro algebra and gap- Virasoro algebras by utilizing restricted modules over their positive part subalgebras, yielding novel results particularly for the mirror Heisenberg-Virasoro algebra when .
This paper investigates the behavior of Galois periods under the local theta correspondence for even orthogonal and symplectic groups by comparing their multiplicities, constructing explicit transfer maps, and establishing both adjoint and relative character relations.
This paper proves that augmented admissible sets in Iwahori-Weyl groups are dual EL-shellable, thereby resolving a conjecture of Görtz and establishing the Cohen-Macaulayness of special fibers for local models with parahoric level structure—including previously open cases in residue characteristic 2 and non-reduced root systems—through a characteristic-free, intrinsic construction that yields an explicit shelling and inductive building procedure.
This paper provides a detailed Lie-algebraic analysis of the Heisenberg-Weyl Lie algebra by constructing explicit unitary intertwining operators for tensor products of its Schrödinger representations and proving that finite-dimensional irreducible representations of the symplectic Lie algebra yield a large family of finite-dimensional, nonunitary indecomposable representations when restricted to .
This paper extends the theory of compatible Poisson brackets and Poisson-commutative subalgebras to reductive Lie algebras decomposed into two complementary solvable horospherical subalgebras, while also deriving results related to the Adler-Kostant-Symes theory.
This paper constructs a mutation cone and a corresponding wall-and-chamber structure for maximal modifying modules over 3-dimensional Gorenstein isolated singularities, proving that the tilting-noetherian property holds if and only if all such modules are mutation-connected, and establishing a regular covering map from a specific subspace of Bridgeland stability conditions to the complexified mutation cone to describe the associated autoequivalence group.
This paper proves that the Hochschild cohomology ring of any self-injective Nakayama algebra is a Batalin-Vilkovisky algebra, thereby demonstrating that the semisimplicity condition on the Nakayama automorphism required in previous results is not necessary, while also correcting inaccuracies found in existing literature.
The paper establishes that the Kazhdan-Lusztig category of W-algebras associated with simple, simply-laced Lie algebras at irrational levels is braided tensor equivalent to the corresponding Kazhdan-Lusztig category of affine vertex algebras via quantum Hamiltonian reduction.
This paper establishes a stability theorem for minimal projective resolutions of modules over finite metric posets by proving that a newly defined bottleneck distance between resolutions is bounded above by the Galois transport distance, thereby generalizing classical bottleneck stability to multiparameter persistence and providing a stability framework for Möbius homology.
This paper generalizes the reflection theory of Nichols algebras to arbitrary coquasi-Hopf algebras with bijective antipode by establishing a braided monoidal equivalence that links finite-dimensional irreducible Yetter-Drinfeld modules admitting all reflections to semi-Cartan graphs, a framework applied to prove that a specific rank three example constitutes an affine Nichols algebra.
This paper constructs a diagrammatic categorification of the spherical module over the Hecke algebra, establishes a basis for its morphism spaces, and proves its equivalence to an existing algebraic spherical category.