Standard domino tableaux and asymptotic Hecke algebras
Unipotent representations and Dixmier algebras
A remark on differential operator algebras and an equivalence of categories
Left cells and domino tableaux in classical Weyl groups
An algebraic proof of the PRV conjecture for very regular weights.
Rings of regular functions on nilpotent orbits and their covers.
Classes of Commutative Clean Rings
Let be a commutative ring with identity and an ideal of . is said to be - if for every element there is an idempotent such that is a unit and belongs to . A filter of ideals, say , of is if for each there is a finitely generated ideal such that . We characterize -clean rings for the ideals , , , and , in terms of the frame of multiplicative Noetherian filters of ideals of , as well as in terms of more classical ring properties.
Rigid extensions of -groups of continuous functions
Let , and denote the -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space , respectively. Characterizations are given for the extensions to be rigid, major, and dense.
When has a clopen -base
It is our aim to contribute to the flourishing collection of knowledge centered on the space of minimal prime subgroups of a given lattice-ordered group. Specifically, we are interested in the inverse topology. In general, this space is compact and , but need not be Hausdorff. In 2006, W. Wm. McGovern showed that this space is a boolean space (i.e. a compact zero-dimensional and Hausdorff space) if and only if the -group in question is weakly complemented. A slightly weaker topological property...
-points vs -points and -points
In a Tychonoff space , the point is called a -point if every real-valued continuous function on can be extended continuously to . Every point in an extremally disconnected space is a -point. A classic example is the space consisting of the countable ordinals together with . The point is known to be a -point as well as a -point. We supply a characterization of -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a -point....
Unique -closure for some -groups of rational valued functions
Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct -closures. Here, we find a reasonably large class with unique and perfectly describable -closure, the class of archimedean -groups with weak unit which are “-convex”. ( is the group of rationals.) Any is -convex and its unique -closure is the Alexandroff algebra of functions on defined from the clopen sets; this is sometimes .
The regular topology on
Hewitt [Rings of real-valued continuous functions. I., Trans. Amer. Math. Soc. 64 (1948), 45–99] defined the -topology on , denoted , and demonstrated that certain topological properties of could be characterized by certain topological properties of . For example, he showed that is pseudocompact if and only if is a metrizable space; in this case the -topology is precisely the topology of uniform convergence. What is interesting with regards to the -topology is that it is possible, with...
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