Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians.

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dc.contributor.advisor Hunziker, Markus, 1968- Pruett, W. Andrew.
dc.contributor.other Baylor University. Dept. of Mathematics. en 2010-05
dc.description.abstract We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first case, an abbreviated computation of relative R-polynomials. From this, we show that these polynomials can be obtained from unlabelled intervals, and more generally, that Kazhdan-Lusztig polynomials associated to cominuscule flag varieties are combinatorially invariant. In the second case, we are able to provide a list of the rationally smooth Schubert varieties in simply laced affine Grassmannians corresponding to types A, D, and E. The results in this case were obtained independently by Billey and Mitchell in 2008. en
dc.rights Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact for inquiries about permission. en
dc.subject R-polynomials. en
dc.subject Rational smoothness. en
dc.subject Affine Grassmannians. en
dc.subject Relative R polynomials. en
dc.subject Cominuscule flag varieties. en
dc.subject Combinatorial invariance. en
dc.subject Weyl group quotients. en
dc.title Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians. en
dc.type Thesis en Ph.D. en
dc.rights.accessrights Worldwide access en
dc.contributor.department Mathematics. en

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