Related papers: Fake degrees of classical Weyl groups

We give a uniform construction of irreducible polynomial representations of all classical groups, including spin groups, using semistandard domino tableaux. We also give an explicit decomposition of the homogeneous coordinate ring of the…

In this paper, we define a mixed-base number system over a Weyl group of type $D$, the group even-signed permutations. We introduce one-to-one correspondence between positive integers and elements of Weyl groups of type $D$ after…

We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we…

We compute the automorphism groups of some quantized algebras, including tensor products of quantum Weyl algebras and some skew polynomial rings.

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 investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.

In a previous paper, we showed that all the cohomological invariants of Weyl groups are completely determined by their restrictions to the abelian subgroups generated by reflections. Using this principle, we describe all the cohomological…

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…

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…

Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an…

In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra $\mathcal{T}(\mu)$. We prove that the level one global Weyl modules of $\mathcal{T}(\mu)$ are isomorphic to the tensor product of the level one…

We compute the generic degrees of the Ariki--Koike algebras by first constructing a basis of matrix units in the semisimple case. As a consequence, we also obtain an explicit isomorphism from any semisimple Ariki--Koike algebra to the group…

We classify all real three dimensional Lie bialgebras. In each case, their automorphism group as Lie bialgebras is also given.

In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…

We define a subset of the set of special representations of a Weyl group. This subset contains at most one representation.

We show that the bicovariant first order differential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations $V$ of the quantum group enveloping algebra. The corresponding calculus is…

Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbers. The same holds for a Sylow 2-subgroup of C.

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.