Related papers: Order types of reflection orders on affine Weyl gr…

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We…

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r,p,n) and the corresponding…

We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of…

We use the author's combinatorial theory of full heaps (defined in math.QA/0605768) to categorify the action of a large class of Weyl groups on their root systems, and thus to give an elementary and uniform construction of a family of…

We give a new proof of the fact that affine Deligne-Lusztig varieties for an algebraic group of adjoint type, associated with superbasic elements, are of finite type. The proof uses a property of the associated Hecke algebra, which we…

A new class of representations of affine Weyl groups on rational functions are constructed, in order to formulate discrete dynamical systems associated with affine root systems. As an application, some examples of difference and…

In this note, we characterize affine and non-affine Coxeter systems among all Coxeter systems in terms of the structure of their reflection orders. For an infinite irreducible system $(W,S)$, we show that affineness can be characterized in…

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain…

In this work we give a full characterization of sets of multiple polynomial recurrence in Weyl systems, which are ergodic unipotent affine transformations on products of tori and finite abelian groups. In particular, we show that measurable…

We study certain types of ideals in the standard Borel subalgebra of an untwisted affine Lie algebra. We classify these ideals in terms of the root combinatorics and give an explicit formula for the number of such ideals in type $A$. The…

We study the complex reflection groups G(r,p,n). By considering these groups as subgroups of the wreath products Z_r wr S_n, and by using Clifford theory, we define combinatorial parameters and descent representations of G(r,p,n),…

We consider the derived category of coherent sheaves on a complex vector space equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl groups of type A, B, G_2, F_4, as well as the groups…

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…

Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the…

In this note, we identify a natural class of subsets of affine Weyl groups whose Poincare series are rational functions. This class includes the sets of minimal coset representatives of reflection subgroups. As an application, we construct…

For an infinite Coxeter system, one can extend the weak right order to the set of infinite reduced words. This is called limit weak order. In [Transformation Groups 18(1), 2013, 179-231], Lam and Pylyavskyy showed that for affine Weyl…

This manuscript contains tables giving the multiplicities with which irreducible characters of exceptional Weyl groups appear in characters induced from certain reflection subgroups containing maximal parabolic subgroups.

In type A, the q,t-Fuss-Catalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we…

We study graded right coideal subalgebras of Nichols algebras of semisimple Yetter-Drinfeld modules. Assuming that the Yetter-Drinfeld module admits all reflections and the Nichols algebra is decomposable, we construct an injective order…