Let V be a representation of the modular group Γ of dimension p. We show that the Z-graded space H(V ) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra M of classical holomorphic modular forms. We study the nature of H considered as a functor from Γ-modules to graded M-lattices and give some applications, including the calculation of the Hil...

La filtration canonique par les pentes d'un module aux q-différences et le gradué associé. Résumé Nous montrons que le polygone de Newton d'uné equation aux q-différences linéaire ne dépend que du module aux q-différences correspondant. Nous interprétons les classiques résultats de factorisation convergente de Adams-Birkhoff-Guenther en termes d'existence d'une filtration canonique par les pent...

It is proved that if an algebra R over a field can be endowed with a pointed and finite-dimensional .nfiltration such that the associated .n-graded algebra T is semi-commutative, then R is left and right finitely partitive. In order to do this, a multi-variable Poincare! series for every finitely generated graded T-module is considered and it is shown that this Poincare! series is a rational fu...

The blob algebra is a finite-dimensional quotient of the Hecke type B which almost always quasi-hereditary. We construct indecomposable tilting modules for over field characteristic 0 in doubly critical case. Every module maximal highest weight either projective or an extension simple by module. Moreover, every submodule weight. conclude that graded Weyl filtration multiplicities this case are ...

We show that bigrassmannian permutations determine the socle of cokernel an inclusion Verma modules in type $A$. All such socular constituents turn out to be indexed by Weyl group elements from penultimate two-sided cell. Combinatorially, a module $w\in S_n$ into dominant are shown determined essential set $w$ and their degrees graded picture computable terms associated rank function. As applic...

A balanced Cohen-Macaulay algebra is a connected algebra A having a balanced dualizing complex ωA[d] in the sense of Yekutieli (1992) for some integer d and some graded A-A bimodule ωA. We study some homological properties of a balanced Cohen-Macaulay algebra. In particular, we will prove the following theorem: Theorem 0.1. Let A be a Noetherian balanced Cohen-Macaulay algebra, and M a nonzero ...

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a classification of the localizing subcategories of T in terms of subsets of the set of prime ideals in...

In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebra b g. The n-th space of this filtration is spanned with the vectors x1. .. xsv, where xi ∈ b g, s ≤ n and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations....

In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebras ĝ. The n-th space of this filtration is spanned by the vectors x1 . . . xsv, where xi ∈ ĝ, s ≤ n, and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations. F...

There exists a graded algebra Λ acting in a natural way on many modules of 3valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on Λ. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, α) produce eight distinct characters on Λ and eight distinct families of weight functions on chord diagrams. As a consequence we ...