The page can be used in two ways. First, you can have the page generate a random parameter. To do that, enter the size of the desired parameter in the first textbox. This size should be an even number.
After entering this information, click one of the two buttons directly to the right. The Run button will display a randomly-generated parameter and the output of the SU*(2n) Algorithm when applied to that parameter. Alternatively, the Run Steps button will also generate a random parameter, and will show you the intermediate steps of applying the SU*(2n) Algorithm to that parameter.
Pressing Enter while in one of the textboxes will click the Run button to the right. Pressing a button a second time, or a different button, will clear the previous result as it gives you a new result, as will pressing Enter while in a textbox.
You can also enter an input parameter in the textbox labelled "parameter". A parameter is an arrangement of the numbers 1 through n into pairs. A typical parameter looks like 3_4 1_5 2_6. The _ is used to indicate a pair of numbers. This example is a parameter for SU*(6).
To enter a parameter in the parameter textbox, write the parameter as in the example, with spaces separating the pieces of the parameter. Then, use the Run or Run Steps buttons to the right of that box, as above.
This page displays the algorithm for computing annihilators and associated varieties for irreducible Harish-Chandra modules for SU*(2n). The input to the SU*(2n) algorithm is a parameter for the irreducible Harish-Chandra module. For the purposes of this algorithm, a parameter takes the form of an arrangement of the numbers 1, ..., 2n into pairs. A typical parameter looks like 3_4 1_5 2_6. The _ is used to indicate a pair of numbers. The example above is a parameter for SU*(6).
A parameter is determined by its pieces (that is, the number pairs). Unlike in a permutation, the order of the pieces doesn't matter. We will list the pieces in increasing numerical order, where this increasing order disregards the first number of any number pair, and just uses the second number to find its place. (The example parameter above is in this order.) The pieces of the parameter are used by the algorithm in this order.
The output of the SU*(2n) algorithm is a single tableau, such as is output by the Robinson-Schensted algorithm. In addition, the rows of the tableau have even length. With this restriction, the algorithm is a bijection.
The output tableau corresponds to the primitive ideal which is the annihilator of the irreducible Harish-Chandra module associated to the parameter. For SU*(2n), the associated variety of this Harish-Chandra module is determined by the shape of the output tableau. For this group, there is no need for a second tableau to describe the associated variety.
Reference: Garfinkle, Devra. "The Annihilators of Irreducible Harish-Chandra Modules for SU(p,q) and Other Type An-1 Groups", American Journal of Mathematics, Vol. 115, No. 2 (Apr., 1993), pp. 305-369, Stable URL: http://www.jstor.org/stable/2374861