84 papers
This paper classifies differential operators between spaces of weighted densities in the superdimension setting, effectively superizing a previous result on modular forms and identifying open problems in the field.
This paper introduces the framework of "fat Lie theory" to establish a one-to-one correspondence between fat extensions and abstract 2-term representations up to homotopy, while demonstrating that fat extensions of groupoids correspond to general linear PB-groupoids and core extensions to vertically/horizontally core-transitive double groupoids, thereby upgrading existing correspondences to equivalences of categories.
This paper characterizes primitive elements in the Ringel-Hall algebra of a tame hereditary algebra associated with a quiver with automorphism, providing a generalized description that improves upon previous results for tame quivers and constructing an explicit basis for the space of primitive elements via a new identity in the regular subalgebra.
This paper investigates the complex reflection group associated with the octahedral group by determining its irreducible representations and character table, computing the modules of vector-valued invariants for each representation, and deriving explicit dimension formulas for the corresponding rings of invariants.
This paper defines contravariantly infinite subcategories of finitely generated modules over a commutative Noetherian ring and establishes several criteria for such infiniteness specifically in the case where the ring is a local complete intersection.
This paper investigates the irreducible components of fixed point sets within the -character variety of a genus two surface under finite group actions, utilizing the genus two DAHA to identify geometric transitions that yield novel candidates for symmetry-reduced moduli spaces in 4d SCFTs.
This paper investigates the representation theory of shifted super Yangians and finite -superalgebras of type A by establishing a criterion for the finite dimensionality of irreducible modules, deriving an explicit Gelfand-Tsetlin character formula for Verma modules, and proving that the centers of these algebras associated with even nilpotent elements are isomorphic to the center of the universal enveloping superalgebra.
This paper introduces shifted quantum affine symmetric pairs of split simply-laced type and constructs their GKLO representations, providing a complete proof that the proposed formulas define a valid representation.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.
This paper constructs new cotorsion pairs in an abelian category by gluing cotorsion pairs from a recollement's outer components, establishes conditions for their coincidence and completeness, and applies these results to Morita rings while introducing a specific class of recollements with enhanced homological properties.
This paper provides a geometric realization of the universal enveloping algebras of Borcherds-Bozec algebras and certain generalized Kac-Moody algebras by utilizing motivic semi-derived and Bridgeland's Hall algebras associated with quivers with loops and acyclic quivers, respectively.
This paper extends previous results on the structure of the center of finite -algebras to a broader range of prime characteristics and demonstrates that their Zassenhaus varieties are rational affine schemes birationally equivalent to a good transverse slice.
This paper proves that the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories, along with shod algebras, is closed under idempotent quotients, idempotent subalgebras, and -reduction, while also extending the closure of laura, glued, and weakly shod algebras under idempotent quotients.
This paper establishes that for any finite group possessing a faithful irreducible representation, every finite supergroup contains an irreducible representation whose restriction to is faithful and center-preserving, thereby proving that such representations always exist in the induction of a faithful representation of .
This paper proposes and provides evidence for conjectures regarding the simple quotients of tensor products within the representation category of a connected reductive algebraic group over a finite field, specifically verifying these conjectures for the case of .
This paper establishes a Murnaghan-Nakayama rule for the irreducible characters of the cyclotomic Hecke algebra on Shoji's standard elements, providing a direct combinatorial method to compute full character tables, deriving dual iterative formulas, and applying these results to obtain new character sum formulas and orthogonality relations.
This paper establishes an explicit bijection between the orbits of in the affine flag variety and affine -clans, which are interpreted as signed involutions in the affine permutation group, thereby extending the classical parametrization of -orbits by clans to the affine setting.
This paper characterizes the rings of invariants for finite orthogonal groups of plus type in odd characteristic and their corresponding Sylow subgroups in defining characteristic by constructing minimal generating sets, describing their relations, and proving that both rings are Cohen-Macaulay complete intersections.
This paper provides a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at an odd prime power root of unity.
This paper establishes that a Cohen-Macaulay complete local ring with an infinite residue field is uniformly dominant with explicit bounds on its dominant index under various conditions, including codimension 2 non-complete intersections, Burch rings, quasi-fiber product rings, and rings with low multiplicity, thereby recovering and refining existing results on hypersurfaces and specific ring classes.