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Flag Varieties and Interpretations of Young Tableau Algorithms

✍ Scribed by Marc A.A van Leeuwen

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
236 KB
Volume
224
Category
Article
ISSN
0021-8693

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✦ Synopsis

The conjugacy class of nilpotent n = n matrices can be parameterized by partitions of n, and for a nilpotent in the class parameterized by , the variety F F of -stable flags has its irreducible components parameterized by the standard Young tableaux of shape . We indicate how several algorithmic constructions defined for Young tableaux have significance in this context, thus extending Steinberg's result that the relative position of flags generically chosen in the irreducible components of F F parameterized by tableaux P and Q is the permuta-

Ž

. tion associated to P, Q under the Robinson᎐Schensted correspondence. Other constructions for which we give interpretations are Schutzenberger's involution of

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