84 papers
This paper investigates the dimension statistics of representations for finite groups, demonstrating that for reductive groups over finite fields and symmetric groups, quantities such as representation dimensions and conjugacy class sizes exhibit asymptotically constant or log-constant behavior as the field size or group rank tends to infinity.
This paper investigates the split Grothendieck group of a -rigid subcategory within an extriangulated category, establishing isomorphisms between the Grothendieck group of the ambient category and specific subcategory groups for silting and -cluster tilting cases, while also determining the explicit structure of the Grothendieck group for -cluster categories of type .
This paper provides a complete classification of when two continuous wavelet systems associated with matrix groups in two dimensions generate identical scales of coorbit spaces, thereby offering a rigorous framework for comparing their approximation-theoretic properties.
This paper investigates the sum of the squares of irreducible character degrees not divisible by a prime and its relation to the corresponding quantity in a -Sylow normalizer, thereby proving a recent conjecture by E. Giannelli for the case and several other instances.
This paper extends support variety theory from the compact to the non-compact part of a monoidal triangulated category in the noncommutative setting, establishing conditions under which the extended theory detects the zero object and thereby confirming a portion of a conjecture by the second author, Nakano, and Yakimov regarding central cohomological support in stable categories of finite tensor categories.
This paper constructs natural Frobenius structures on two families of rigid irregular -connections, utilizing them to analyze local monodromy, verify Reeder--Yu's predictions on epipelagic Langlands parameters, and confirm the cohomological and physical rigidity conjectures of Heinloth--Ngô--Yun.
This paper establishes an -duality converse to prior work by proving that the -dual of the action of on their tautological representations is the symplectic mirabolic space acting on and its tautological representations, while also formulating a corresponding global conjecture for the categorical theta-correspondence.
The paper demonstrates that Brascamp-Lieb constants are semi-algebraic functions of their feasible data, satisfying a polynomial relation, and extends this algebraicity result to the broader context of quiver Brascamp-Lieb constants associated with bipartite quivers.
This paper adapts methods from complex semisimple Lie algebra theory to establish a root theory for basic simple -graded color Lie algebras, enabling the classification of their finite-dimensional representations through highest weight and complete reducibility theorems under the assumption of a self-centralizing Cartan subalgebra.
This paper constructs exotic Hecke correspondences between the special fibers of PEL-type Shimura varieties with potentially bad reduction by utilizing Pappas-Rapoport splitting models, thereby establishing new geometric Jacquet-Langlands correspondences and verifying generic instances of the Tate conjecture.
This paper investigates homotopy decompositions of classifying spaces of compact connected Lie groups via a relative fiber-cofiber construction, establishing rational sharpness and Cohen-Macaulay properties for the resulting spaces under specific cohomological conditions while providing explicit cohomological and K-theoretic computations for examples involving maximal tori and commuting elements.
This paper constructs a monoidal category of representations for the quantum affine algebra of a simple, simply connected, simply laced algebraic group, whose Grothendieck ring contains a cluster algebra with an initial seed corresponding to the coordinate ring of twisted products of flag varieties, including braid varieties and reduced double Bruhat cells.
This paper establishes that a commutator is a -element for all if and only if is central modulo , a result that generalizes the Baer--Suzuki and Glauberman -theorems and is applied to prove that a conjugacy class satisfying generates a solvable subgroup.
This paper constructs and classifies all differential symmetry breaking operators between principal series representations of the de Sitter and Lorentz groups , proving that all such operators are necessarily differential and constitute "sporadic" cases that cannot be derived from meromorphic families via residue formulas.
This paper proves a conjecture by Trinh and Xue regarding intersections of blocks in cyclotomic Hecke algebras for all exceptional finite reductive groups except , while also proposing and partially confirming generalizations to Suzuki, Ree, non-rational Coxeter, and spetsial complex reflection groups.
This paper investigates the limit shapes and fluctuations of random Young diagrams arising from symplectic group duality by deriving semiclassical orthogonal polynomials via Christoffel transformation from Krawtchouk polynomials and analyzing their asymptotic behavior through an integral representation, thereby overcoming the lack of a free-fermionic representation available in the general linear case.
This paper constructs and provides a complete classification of all differential symmetry breaking operators between specific vector and line bundles over the 3-sphere and 2-sphere, respectively, in the special case where the rank parameter equals the absolute value of the integer .
This paper computes the height filtration and successive minima of the height function associated with a relatively ample line bundle on a flag bundle over a smooth projective curve defined over an algebraically closed field of positive characteristic.
This paper establishes a correspondence between model structures and a single hereditary complete cotorsion pair on weakly idempotent complete extriangulated categories, thereby generalizing previous results by Beligiannis-Reiten and Cui et al., and provides methods to construct such model structures from silting objects and co--structures.
This paper derives the polar-finite decomposition for odd-spin admissible-level characters and establishes new mock theta conjecture-like identities for the corresponding string functions at levels $2/32/5$.