Related papers: The representations of cyclotomic BMW algebras
We classify the finite dimensional irreducible representations of affine Hecke algebras of type B_2 with unequal parameters.
In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2,2p-1,2p-1,2p-1) series of triplet…
Let M(1) be the vertex algebra for a single free boson. We classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators. These subalgebras correspond to the W(2, 2p-1)--algebras with central charge $1- 6…
We give a presentation of the endomorphism algebra $\End_{\cU_q(\fsl_2)}(V^{\otimes r})$, where $V$ is the 3-dimensional irreducible module for quantum $\fsl_2$ over the function field $\C(q^{{1/2}})$. This will be as a quotient of the…
We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root…
We study lowest-weight irreducible representations of rational Cherednik algebras attached to the complex reflection groups G(m,r,n) in characteristic p. Our approach is mostly from the perspective of commutative algebra. By studying the…
Let $ \mathbb{A}$ be a cellular algebra over a field $\mathbb{F}$ with a decomposition of the identity $ 1_{\mathbb{A}} $ into orthogonal idempotents $ e_i$, $i \in I$ (for some finite set $I$) satisfying some properties. We describe the…
The modular representation theory of the queer Lie superalgebra q(n) over characteristic p>2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters and a criterion for the…
By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…
Let U be the quantised enveloping algebra associated to a Cartan matrix of finite type. Let W be the tensor product of a finite list of highest weight representations of U. Then the centraliser algebra of W has a basis called the dual…
Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the binary case is thus the first nontrivial case. This paper sees…
We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford…
The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented…
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras…
Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is…
We prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type $B$ are unions of combinatorial cells (defined using the domino insertion algorithm).
In this article, we give a family of examples of algebras, showing that for every $n \geq 2$ and $m \geq 0$, there is an algebra displaying a path of n irreducible morphisms between indecomposable modules whose composite lies in the…
We construct gradings on the simple modules of 2-boundary Temperley--Lieb algebras and symplectic blob algebras by realising the latter algebras as quotients of Varagnolo--Vasserot's orientifold quiver Hecke algebras. We prove that the…
We show that the affine Brauer algebras are affine cellular algebras in the sense of Koenig and Xi.