Related papers: On Extensions Between Verma Modules

Let $\mathfrak{g}=\mathfrak{g}_{\bar0}+\mathfrak{g}_{\bar1}$ be a basic classical Lie superalgebra over $\mathbb{C}$, and $e=e_{\theta}\in\mathfrak{g}_{\bar0}$ with $-\theta$ being a minimal root of $\mathfrak{g}$. Set $U(\mathfrak{g},e)$…

For any complex parameters a,b, the W(a,b) algebra is the Lie algebra with basis {L_i,W_i|i\in Z}, and relations [L_i,L_j]=(j-i)L_{i+j}, [L_i,W_j]=(a+j+bi)W_{i+j},[W_i,W_j]=0. In this paper, indecomposable modules of the intermediate series…

We observe that the join operation for the Bruhat order on a Weyl group agrees with the intersections of Verma modules in type $A$. The statement is not true in other types, and we propose a conjectural statement of a weaker correspondence.…

We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They are formal analogues of Fourier-Jacobi expansions of Siegel modular forms. From our result and a theorem of Wei Zhang, we deduce Kudla's…

In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properties of the prime ideals and their…

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra not of the type A(2k,2l)^{(4)}. We obtain the character formula for a simple module with a generic…

Using principal series Harish-Chandra modules, local cohomology with support in Schubert cells and twisting functors we construct certain modules parametrized by the Weyl group and a highest weight in the subcategory O of the category of…

The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective finite dimensional algebra is finite. In \cite{Yam}, Yamagata stated the stronger conjecture that the dominant dimension of a non-selfinjective finite…

We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective, then its underlying module over the the base ring is Gorenstein projective; the converse holds if the Frobenius extension is either…

The main result of this paper is an instance of the conjecture made by Gouvea and Mazur (Math. Res. Lett., 1995) which asserts that for certain values of r the space of r-overconvergent p-adic modular forms of tame level N and weight k…

We propose a refined version of the Beilinson-Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of the relevant p-adic Abel-Jacobi map to certain combinations…

With this paper we start the study of reducible representations of the Jacobi algebra with the ultimate goal of constructing differential operators invariant w.r.t. the Jacobi algebra. In this first paper we show examples of the low level…

For an abelian category $\mathcal{A}$, we establish the relation between its derived and extension dimensions. Then for an artin algebra $\Lambda$, we give the upper bounds of the extension dimension of $\Lambda$ in terms of the radical…

Let $p>2$ be a prime. Under mild assumptions, we prove the Iwasawa main conjecture of Kato, for modular forms with general weight and conductor prime to $p$.

A conjecture regarding the structure of expander graphs is discussed.

We address a question posed by Ono, prove a general result for powers of an arbitrary prime, and provide an explanation for the appearance of higher congruence moduli for certain small primes. One of our results coincides with a recent…

We study the extensions of two left modules $W_1, W_2$ for a meromorphic open-string vertex algebra $V$. We show that the extensions satisfying some technical but natural convergence conditions are in bijective correspondence to the first…

In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. In one direction, we show that the conjecture on the existence of complements implies the…

Highest weight modules of the double affine Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal…