Related papers: Superspecial representations of Weyl groups
The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special…
We compute the Weyl group (in the sense of Segal) of the group of holomorphic isometries of a K\"ahler toric manifold with real analytic K\"ahler metric.
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
We define a property sub-representability and we give a complete characterisation of sub-representability of posets.
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
We extend the Weil representation of infinite-dimensional symplectic group to a representation a certain category of linear relations.
In this paper, we offer a presentation for the Weyl group of an affine reflection system $R$ of type $A_1$ as well as a presentation for the so called hyperbolic Weyl group associated with an affine reflection system of type $A_1$. Applying…
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.
We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.
Super Weyl group plays an important role in the study of representations of basic classical Lie superalgebras. The Coxeter graphs for super Weyl groups of basis classical Lie superalgebras have been given in \cite{CLS}, where the authors…
We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.
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 determine the finite groups whose real irreducible representations have different degrees.
We consider the finite Weyl groups of classical type -- $W(A_{r})$ for $r \geq 1$, $W(B_{r}) = W(C_{r})$ for $r \geq 2$, and $W(D_{r})$ for $r \geq 4$ -- as supergroups in which the reflections are of odd superdegree. Viewing the…
An introductory review of algebraic classification of the Weyl tensor and algebraically special solutions in higher dimensions.
This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary…
We classify closed abelian subgroups of a compact simple Lie group of adjoint type and of type E having centralizer of the same dimension as the dimension of the subgroup and describe Weyl groups of maximal abelian subgroups.
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
We show that various invariants of a unipotent conjugacy class in a connected semisimple group can be recovered purely in terms of data involving the Weyl group.
The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…