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Winter 2014 Cohomological consequences of the pattern map
Praise Adeyemo, Frank Sottile
Illinois J. Math. 58(4): 997-1008 (Winter 2014). DOI: 10.1215/ijm/1446819296


Billey and Braden defined maps on flag manifolds that are the geometric counterpart of permutation patterns. A section of their pattern map is an embedding of the flag manifold of a Levi subgroup into the full flag manifold. We give two expressions for the induced map on cohomology. One is in terms of generators and the other is in terms of the Schubert basis. We show that the coefficients in the second expression are naturally Schubert structure constants and therefore positive. Similar results hold for $K$-theory, generalizing known formulas in type $A$ for cohomology and $K$-theory.


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Praise Adeyemo. Frank Sottile. "Cohomological consequences of the pattern map." Illinois J. Math. 58 (4) 997 - 1008, Winter 2014.


Received: 3 September 2014; Revised: 20 April 2015; Published: Winter 2014
First available in Project Euclid: 6 November 2015

zbMATH: 1326.14116
MathSciNet: MR3421594
Digital Object Identifier: 10.1215/ijm/1446819296

Primary: 05E05, 14M15, 14N15

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign


Vol.58 • No. 4 • Winter 2014
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