A PieriChevalley formula in the Ktheory of a bundle
Authors:
Harsh Pittie and Arun Ram
Journal:
Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 102107
MSC (1991):
Primary 14M15; Secondary 14C35, 19E08
Published electronically:
July 14, 1999
MathSciNet review:
1701888
Fulltext PDF Free Access
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Additional Information
Abstract: Let be a semisimple complex Lie group, a Borel subgroup, and a maximal torus of . The projective variety is a generalization of the classical flag variety. The structure sheaves of the Schubert subvarieties form a basis of the Ktheory and every character of gives rise to a line bundle on . This note gives a formula for the product of a dominant line bundle and a Schubert class in . This result generalizes a formula of Chevalley which computes an analogous product in cohomology. The new formula applies to the relative case, the Ktheory of a bundle over a smooth base , and is presented in this generality. In this setting the new formula is a generalization of recent results of Fulton and Lascoux.
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Additional Information
Harsh Pittie
Affiliation:
Department of Mathematics, Graduate Center, City University of New York, New York, NY 10036
Arun Ram
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544
Email:
rama@math.princeton.edu
DOI:
http://dx.doi.org/10.1090/S1079676299000670
PII:
S 10796762(99)000670
Received by editor(s):
February 9, 1999
Published electronically:
July 14, 1999
Additional Notes:
Research supported in part by National Science Foundation grant DMS9622985.
Communicated by:
Efim Zelmanov
Article copyright:
© Copyright 1999
American Mathematical Society
