Related papers: Jantzen Conjecture for singular characters

We study the values taken by the Riemann zeta-function $\zeta$ on discrete sets. We show that infinite vertical arithmetic progressions are uniquely determined by the values of $\zeta$ taken on this set. Moreover, we prove a joint discrete…

We introduce more properties of forcing notions which imply that their lambda-support iterations are lambda-proper, where lambda is an inaccessible cardinal. This paper is a direct continuation of section A.2 of math.LO/0210205. As an…

We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of $M_n(\mathbb{C})$ admits an orthonormal unitary…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…

The aim of the paper is to study the group schemes $G:=\operatorname{SL}_{2, A}, \operatorname{GL}_{2,A}$ and universal Clebsch-Gordan filtrations. Here $A$ is a field or any commutative ring. If $V:=A\{e_1,e_2\}$ is the free rank $2$…

Let $\mathcal{D}$ be the Drinfeld double of the bosonization ${\mathfrak B}(V)\#\Bbbk G$ of a finite-dimensional Nichols algebra ${\mathfrak B}(V)$ over a finite group $G$. It is known that the simple $\mathcal{D}$-modules are parametrized…

A known result for the finite general linear group $\GL(n,\FF_q)$ and for the finite unitary group $\U(n,\FF_{q^2})$ posits that the sum of the irreducible character degrees is equal to the number of symmetric matrices in the group. Fulman…

Let $p$ be a prime number. We prove that the $P=W$ conjecture for $\mathrm{SL}_p$ is equivalent to the $P=W$ conjecture for $\mathrm{GL}_p$. As a consequence, we verify the $P=W$ conjecture for genus 2 and $\mathrm{SL}_p$. For the proof, we…

In this article, we investigate conditional large values of quadratic Dirichlet character sums. We prove some Omega results of quadratic character sums under the assumption of the generalized Riemnn hypothesis, which are as sharp as…

We verify a conjecture of Etingof and Ostrik, stating that an algebra object in a finite tensor category is exact if and only if it is a finite direct product of simple algebras. Towards that end, we introduce an analogue of the Jacobson…

In this paper, we prove a few lemmas concerning Fibonacci numbers modulo primes and provide a few statements that are equivalent to Wall-Sun-Sun Prime Conjecture. Further, we investigate the conjecture through heuristic arguments and…

We prove an analog of the disintegration theorem for tracial von Neumann algebras in the setting of elementary equivalence rather than isomorphism, showing that elementary equivalence of two direct integrals implies fiberwise elementary…

The notions of permutable and weak-permutable convergence of a series $\sum_{n=1}^{\infty}a_{n}$ of real numbers are introduced. Classically, these two notions are equivalent, and, by Riemann's two main theorems on the convergence of…

In 2022, Huh-Matherne-M\'esz\'aros-St. Dizier showed that normalized Schur polynomials are Lorentzian, thereby yielding their continuous (resp. discrete) log-concavity on the positive orthant (resp. on their support, in type $A$ root…

We classify the finite irreducible modules over the conformal superalgebra $K'_{4}$ by their correspondence with finite conformal modules over the associated annihilation superalgebra $\mathcal A(K'_{4})$. This is achieved by a complete…

We investigate a conjecture to describe the characters of large families of RCFT's in terms of contour integrals of Feigin-Fuchs type. We provide a simple algorithm to determine the modular S-matrix for arbitrary numbers of characters as a…

While examples of Ramanujan-type congruences are amply available via their relation to Hecke operators, it remains unclear which of them should be considered of combinatorial origin and which of them are mere artifacts of the connection…

We prove a conjecture of Casselman and Shahidi stating that the unique irreducible generic subquotient of a standard module is necessarily a subrepresentation for a large class of connected quasi-split reductive groups, in particular for…

Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-projective generator with vanishing self-extensions in all positive degrees, is shown to be invariant under certain singular equivalences induced by adjoint…

Since techniques used to address the Nivat's conjecture usually relies on Morse-Hedlund Theorem, an improved version of this classical result may mean a new step towards a proof for the conjecture. In this paper, considering an alphabetical…