Quiver Varieties, Category O for Rational Cherednik Algebras, and Hecke Algebras

We relate the representations of the rational Cherednik algebras associated with the complex reflection group µℓ ≀ Sn to sheaves on Nakajima quiver varieties associated with extended Dynkin graphs via a Z-algebra construction. This is done so that as the parameters defining the Cherednik algebra vary, the stability conditions defining the quiver variety change. This construction motivates us to use the geometry of the quiver varieties to interpret the ordering function (the c-function) used to define a highest weight structure on category O of the Cherednik algebra. This interpretation provides a natural partial ordering on O which we expect will respect the highest weight structure. This partial ordering has appeared in a conjecture of Yvonne on the composition factors in O and so our results provide a small step towards a geometric picture for that. We also interpret geometrically another ordering function (the a-function) used in the study of Hecke algebras. (The connection between Cherednik algebras and Hecke algebras is provided by the KZ-functor.) This is related to a conjecture of Bonnafé and Geck on equivalence classes of weight functions for Hecke algebras with unequal parameters since the classes should (and do for type B) correspond to the G.I.T. chambers defining the quiver varieties. As a result anything that can be defined via the quiver varieties

\u3cem\u3eYoungstown\u3c/em\u3e, \u3cem\u3eHamdan\u3c/em\u3e, and Inherent Emergency Presidential Policymaking Powers

This brief article explores the contribution that Hamdan v Rumsfeld may have made to clarifying what should happen in the large interstices of the rules created by the Youngstown case for determining the validity of claims of Presidential power. It offers its own view of the scope of Presidential powers in extreme emergencies involving the incapacitation of the legislative branch

Wikis in Tuple Spaces

We consider storing the pages of a wiki in a tuple space and the effects this might have on the wiki experience. In particular, wiki pages are stored in tuples with a few identifying values such as title, author, revision date, content, etc. and pages are retrieved by sending the tuple space templates, such as one that gives the title but nothing else, leaving the tuple space to resolve to a single tuple. We use a tuple space wiki to avoid deadlocks, infinite loops, and wasted efforts when page edit contention arises and examine how a tuple space wiki changes the wiki experience.Comment: To appear at WMSCI 200

Some vision algorithms

The ability to determine the contents of a scene by a machine has obvious applications. There are reasons for seeking horizontal, vertical and diagonal line segments of varying lengths in order to interpret the content of a scene. Such line segments aid in determining edges that determine the boundaries of objects within the scene. Algorithms for each of the above as well as for data compacting are presented

Solar prediction and intelligent machines

The solar prediction program is aimed at reducing or eliminating the need to throughly understand the process previously developed and to still be able to produce a prediction. Substantial progress was made in identifying the procedures to be coded as well as testing some of the presently coded work. Another project involves work on developing ideas and software that should result in a machine capable of learning as well as carrying on an intelligent conversation over a wide range of topics. The underlying idea is to use primitive ideas and construct higher order ideas from these, which can then be easily related one to another

Influence of upstream flow discontinuities on the acoustic power radiated by a model air jet

Effect of upstream flow discontinuities on acoustic power radiated by model air je

Dynamic pattern matcher using incomplete data

This invention relates generally to pattern matching systems, and more particularly to a method for dynamically adapting the system to enhance the effectiveness of a pattern match. Apparatus and methods for calculating the similarity between patterns are known. There is considerable interest, however, in the storage and retrieval of data, particularly, when the search is called or initiated by incomplete information. For many search algorithms, a query initiating a data search requires exact information, and the data file is searched for an exact match. Inability to find an exact match thus results in a failure of the system or method

Tight-fill fruit packing /

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