Related papers: On Extensions Between Verma Modules

In the present paper we study the representations of the Jacobi algebra. More concretely, we define, analogously to the case of semi-simple Lie algebras, the Verma modules over the Jacobi algebra ${\cal G}_2$. We study their reducibility…

We extend the results of [CGLS22] to higher weight modular forms and prove a rank $0$ Tamagawa number formula (also known as the Bloch-Kato conjecture) for modular forms at good Eisenstein primes, under some technical assumption on periods.…

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness…

In this article we prove a version of Kolyvagin's conjecture for modular forms at non-ordinary primes. In particular, we generalize the work of Wang on a converse to a higher weight Gross-Zagier-Kolyvagin theorem in order to prove the…

A notion of generalized highest weight modules over the high rank Virasoro algebras is introduced, and a theorem, which was originally given as a conjecture by Kac over the Virasoro algebra, is generalized. Mainly, we prove that a simple…

We show that subsingular vectors exist in Verma modules over W(2,2), and present a subquotient structure of these modules. We prove conditions for irreducibility of a tensor product of intermediate series module with the highest weight…

An extension $B\subset A$ of finite dimensional algebras is bounded if the $B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$. We show…

We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's characteristic varieties. We show that an…

In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f in S_k(N) satisfying certain conditions, we construct a map from the Heegner points of level N to a…

Irreducibilities of Verma modules over a class of Block type Lie algebras are completely determined. The approach developed in the present paper can be used to deal with non-weight modules.

In this paper we show that a conjecture of Stephen Yau on highest weights of invariant Jacobians is true for arbitrary connected semisimple algebraic groups.

A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules…

In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.

In the first part of this paper the projective dimension of the structural modules in the BGG category $\mathcal{O}$ is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an…

In the paper we present a different proof of the theorem of B. L. Feigin and D. B. Fuchs about the structure of Verma modules over Virasoro algebra. We state some new results about the structure of Verma modules over Neveu-Schwarz. The…

We generalize the work of Bertolini and Darmon on the anticyclotomic main conjecture for weight two forms to higher weight modular forms.

Let $F$ be a totally real field of degree $n$ and $p$ an odd prime. We prove the $p$-part of the integral Gross--Stark conjecture for the Brumer--Stark $p$-units living in CM abelian extensions of $F$. In previous work, the first author…

In this paper, we prove under mild hypotheses the Iwasawa main conjectures of Lei--Loeffler--Zerbes for modular forms of weight $2$ at non-ordinary primes. Our proof is based on the study of the two-variable analogues of these conjectures…

For sigma-PWB extensions, we extend to modules the theory of Gr\"obner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative sigma-PWB extension, we compute the module of syzygies of a submodule of…

We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings…