Related papers: Graded decomposition numbers for cyclotomic Hecke …
Let $S_\lambda$ denote the Specht module defined by Dipper and James for the Iwahori-Hecke algebra $\mathscr{H}_n$ of the symmetric group $\mathfrak{S}_n$. When $e=2$ we determine the decomposability of all Specht modules corresponding to…
The graded Specht module $S^\lambda$ for a cyclotomic Hecke algebra comes with a distinguished generating vector $z^\lambda\in S^\lambda$, which can be thought of as a "highest weight vector of weight $\lambda$". This paper describes the…
These are lecture notes prepared for London Mathematical Society Symposium "Quantum Groups" held in Durham 19-29 July 1999. We give a survey on cyclotomic Hecke algebras. These algebras have been studied by Dipper, James, Malle, Mathas and…
In this paper, we study an irreducible decomposition structure of the $\Dc$-module direct image $\pi_+(\Oc_{ \bC^n})$ for the finite map $\pi: \bC^n \to \bC^n/ ({\Sc_{n_1}\times \cdots \times \Sc_{n_r}}).$ We explicitly construct the simple…
We give a presentation of localized affine and degenerate affine Hecke algebras of arbitrary type in terms of weights of the polynomial subalgebra and varied Demazure-BGG type operators. We offer a definition of a graded algebra…
We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees…
We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring $A=\mathbb Z[q^{1/2},q^{-1/2}]$ where $q$ is an indeterminate) using…
This paper shows that certain decomposition numbers for the Hecke algebras and q-Schur algebras at different roots of unity in characteristic zero are equal. To prove our results we first establish the corresponding theorem for the…
We introduce a class of polynomials that we call fused Specht polynomials and use them to characterize irreducible representations of the fused Hecke algebra with parameter $q=-1$ in the space of polynomials. We apply the fused Specht…
We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting the basic ribbon product rule in NSym via concatenation and…
We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…
We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the…
We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirming a conjecture of Leclerc and Thibon.
Over fields of characteristic $2$, Specht modules may decompose and there is no upper bound for the dimension of their endomorphism algebra. A classification of the (in)decomposable Specht modules and a closed formula for the dimension of…
We develop a graded version of the theory of cyclotomic q-Schur algebras, in the spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki on q-Schur algebras. As an application, we identify the coefficients of the canonical…
We construct indecomposable modules for the 0-Hecke algebra whose characteristics are the dual immaculate basis of the quasi-symmetric functions.
The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…
In this paper we study the vertices of indecomposable Specht modules for symmetric groups. For any given indecomposable non-projective Specht module, the main theorem of the article describes a family of p-subgroups contained in its vertex.…
We present (with proof) a new family of decomposable Specht modules for the symmetric group in characteristic 2. These Specht modules are labelled by partitions of the form $(a,3,1^b)$, and are the first new examples found for thirty years.…
We generalize Soergel's tilting algorithm to singular weights and deduce from this the validity of the Lascoux-Leclerc-Thibon conjecture on the connection between the canonical basis of the basic submodule of the Fock module and the…