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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<link rel="stylesheet" href="common/pageStyles.css"/>
<style type="text/css">
section {
margin: 50px;
}
section#description {
font-size: 1.2em;
}
div {
margin: 10px 10px 10px 14px;
}
a.pagelink {
margin-right: 30px;
}
h2 {
margin: 20px 10px 5px 10px;
}
.toggleButton {
margin-left: 10px;
}
</style>
<script>
function toggleDiv(button) {
let text = button.innerHTML;
let number = button.id[11];
let divName = "AboutDiv" + number;
if (text[0] == "H") {
let newText = text.slice(5);
button.innerHTML = newText;
}
else {
button.innerHTML = "Hide " + text;
}
let div = document.getElementById(divName);
this.showHide(div);
}
function showHide(info) {
let divToToggle;
if (typeof(info) == "string") {
divToToggle = document.getElementById(info);
} else {
divToToggle = info;
}
if (divToToggle.style.display == 'block') {
divToToggle.style.display = 'none';
} else {
divToToggle.style.display = 'block';
}
}
</script>
<title>Tableaux Algorithms</title>
</head>
<body>
<section id="description">
The pages below display the algorithms which I've discovered and studied (plus the original Robinson-Schensted algorithm).
You can download the files from the repository: <a href="https://github.com/devragj/devragj.github.io" target="_blank">GitHub Pages Repository</a>.
I welcome feedback. Please contact me at devra.johnson at verizon.net.
</section>
<section>
<h2>Robinson-Schensted Algorithm
<span class="infoButtons">
<button type="button" class="toggleButton" id="AboutButton1" onclick="toggleDiv(this)">About These Pages</button>
</span>
</h2>
<div class="infoDiv" id="AboutDiv1" style="display:none">
<p>
These two pages illustrate the well-known Robinson-Schensted algorithm.
This algorithm starts with a permutation and produces a pair of tableaux.
The left tableau is called the insertion or bumping tableau.
The right tableau is called the recording tableau.
The first page shows either the final result of the algorithm or the result of each step of adding one number to the tableaux pair.
The second page has an animation of the bumping procedure.
</p>
</div>
<div>
<a class="pagelink" href="TypeA/RobinsonSchensted.html">Robinson-Schensted Algorithm</a>
</div>
<div>
<a class="pagelink" href="TypeA/RobinsonSchenstedAnimate.html">Robinson-Schensted Algorithm Animated</a>
</div>
</section>
<section>
<h2>Domino Robinson-Schensted Algorithm
<span class="infoButtons">
<button type="button" class="toggleButton" id="AboutButton2" onclick="toggleDiv(this)">About These Pages</button>
</span>
</h2>
<div class="infoDiv" id="AboutDiv2" style="display:none">
<p>
These pages illustrate the domino Robinson-Schensted algorithm.
This algorithm starts with a signed permutation and produces a pair of domino tableaux.
As with the ordinary Robinson-Schensted algorithm, the left tableau is the insertion, or bumping, tableau.
The right tableau is the recording tableau.
The first page shows either the final result of the algorithm or the result of each step of adding one number to the tableaux pair.
The second page has an animation of the bumping procedure.
</p>
<p>
The domino Robinson-Schensted algorithm is the first step in classifying Kazhdan-Lusztig cells (equivalently, classifying primitive ideals).
After that, we need to apply another procedure (called moving through cycles) to produce tableaux with a special shape.
To do that, we need first to place each tableau on a grid.
That's shown in the third page.
The fourth page shows the result of making the tableaux special.
The pages in the next section show more about the procedure of moving through cycles.
</p>
</div>
<div>
<a class="pagelink" href="TypeBCD/DominoRobinsonSchensted.html">Domino Robinson-Schensted Algorithm</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/DominoRobinsonSchenstedAnimate.html">Domino Robinson-Schensted Algorithm Animated</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/DominoRobinsonSchenstedGrids.html">Domino Robinson-Schensted Algorithm, with Grid</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/DominoRobinsonSchenstedSpecial.html">Domino Robinson-Schensted Algorithm, Then Make Special</a>
</div>
</section>
<section>
<h2>Moving Through Open Cycles
<span class="infoButtons">
<button type="button" class="toggleButton" id="AboutButton3" onclick="toggleDiv(this)">About These Pages</button>
</span>
</h2>
<div class="infoDiv" id="AboutDiv3" style="display:none">
<p>
The first four pages demonstrate the procedure of moving a tableau through an open cycle.
This procedure is used in the classification of Kazhdan-Lusztig cells and also in some of the Harish-Chandra algorithms (shown in the pages of the next section).
</p>
<p>
When you have a pair of tableaux of the same shape, you move through an extended open cycle to obtain another pair of tableaux of the shape.
The last three pages show this procedure.
</p>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesAnimateCopy.html">Animate Cycles Copy</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesAnimateInPlace.html">Animate Cycles In Place</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesAnimateSpecial.html">Animate Cycles Special</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesHover.html">View Cycles</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesAnimatePairCopy.html">Animate Extended Cycles Copy</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesAnimatePairInPlace.html">Animate Extended Cycles In Place</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/CyclesAnimatePairSpecial.html">Animate Extended Cycles Special</a>
</div>
</section>
<section>
<h2>Harish-Chandra Module Algorithms
<span class="infoButtons">
<button type="button" class="toggleButton" id="AboutButton4" onclick="toggleDiv(this)">About These Pages</button>
</span>
</h2>
<div class="infoDiv" id="AboutDiv4" style="display:none">
<p>
The algorithms in these pages are used for computing annihilators of irreducible Harish-Chandra modules (equivalently, Kazhdan-Lusztig-Vogan cells.)
</p>
<p>
For the last algorithm in this series (still experimental), see <a class="pagelink" href="https://devragj.github.io/SOpq-Algorithm/index.html">SO(p,q) and Sp(n,ℝ) Algorithms</a>
</p>
</div>
<div>
<a class="pagelink" href="TypeA/SUpqAlgorithm.html">SU(p,q) Algorithm</a>
</div>
<div>
<a class="pagelink" href="TypeA/SUStar2nAlgorithm.html">SU*(2n) Algorithm</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/SppqAlgorithm.html">Sp(p,q) Algorithm</a>
</div>
<div>
<a class="pagelink" href="TypeBCD/SOStar2nAlgorithm.html">SO*(2n) Algorithm</a>
</div>
</section>
</body>
</html>