Related papers: Certain subgroups of Weyl groups are split

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid…

We define categories $\mathcal{O}^w$ of representations of Borel subalgebras $\mathcal{U}_q\mathfrak{b}$ of quantum affine algebras $\mathcal{U}_q\hat{\mathfrak{g}}$, which come from the category $\mathcal{O}$ twisted by Weyl group elements…

In this note, we introduce a new concept of a {\it generalized algebraic rational identity} to investigate the structure of division rings. The main theorem asserts that if a non-central subnormal subgroup $N$ of the multiplicative group…

Let K be the quotient field of a complete local domain of dimension 2 with a separably closed residue field. Let G be a finite group of order not divisible by char(K). Then G is admissible over K if and only if its Sylow subgroups are…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

A Weyl group W is a union of strata (certain subsets which are unions of conjugacy classes) which are the nonempty fibres of a map from W to the set of irreducible representations of W. We give an explicit description of strata in terms of…

We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup $GL(m|n)$. Furthermore,…

We compute all sections of the finite Weyl group, that satisfy the braid relations, in the case that G is an almost-simple connected reductive group defined over an algebraically closed field. We then demonstrate that this set of sections…

In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special…

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 consider the fine grading of $sl(n,\mb C)$ induced by tensor product of generalized Pauli matrices in the paper. Based on the classification of maximal diagonalizable subgroups of $PGL(n,\mb C)$ by Havlicek, Patera and Pelantova, we…

We prove that the Weyl algebra over $\mathbb{C}$ cannot be a fixed ring of any domain under a nontrivial action of a finite group by algebra automorphisms, thus settling a 30-year old problem. In fact, we prove the following much more…

This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the…

The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields.…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.

We construct a complex linear Weil representation $\rho$ of the generalized special linear group $G={\rm SL}_*^{1}(2,A_n)$ ($A_n=K[x]/\langle x^n\rangle$, $K$ the quadratic extension of the finite field $k$ of $q$ elements, $q$ odd), where…

The special representations of a Weyl group can be regarded as the vertices of a graph with an involution i such that any edge e has the following property: either e or i(e) joins two vertices whose a-functions differ by 1.

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…

We study completely syndetic (CS) sets in discrete groups - subsets that for every natural n admit finitely many left translates that jointly cover every n-tuple of group elements. While for finitely-generated groups, the non-virtually…