Related papers: A Unified Construction of Coxeter Group Representa…

We introduce a concept of a W-graph ideal in a Coxeter group. The main goal of this paper is to describe how to construct a W-graph from a given W-graph ideal. The principal application of this idea is in type A, where it provides an…

We characterize relatively norm compact sets in the regular $C^*$-algebra of finitely generated Coxeter groups using a geometrically defined positive semigroup acting on the algebra.

The present note sketches a theory of constructs.

An introduction and overview of constructive reverse mathematics.

This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…

For weighted group convoltion measure algebra we construct a representation on reflexsive space.

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…

We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

This is the first of a series of papers which define and study structures called rootoids, which are groupoids equipped with a representation in the category of Boolean rings and with an associated 1-cocycle. The axioms for rootoids are…

Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…

We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation. As an application, we show that the characteristic polynomial of a Coxeter multiarrangement with…

We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…

We change the definition of the vertex representations. As a result the vertex representations has one parameter.

We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.

In the recent paper [A14], a geometric realization to minimal representations of simple real Lie groups of non Hermitian type is given, based on the geometric setting introduced in [A11]. We give in this paper a geometric realization to…

We provide every Renner monoids with a monoid presentation, and we introduce a length function which extends the Coxeter length function.

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.